Mixing
What's the difference between an initial value problem and a boundary value problem?
$begingroup$
I don't really see the difference, because in both case we need to determine y and the values of the constants. The only difference is that we give the value of y and y' in the former and the value of either 2 y or 2 y' in the latter.
I solve both problems the same way. I don't really understand the theory, I guess.
ordinary-differential-equations
asked May 18 '13 at 2:54
Gladstone AsderGladstone Asder
5313921
$endgroup$
add a comment |
$begingroup$
I don't really see the difference, because in both case we need to determine y and the values of the constants. The only difference is that we give the value of y and y' in the former and the value of either 2 y or 2 y' in the latter.
I solve both problems the same way. I don't really understand the theory, I guess.
ordinary-differential-equations
asked May 18 '13 at 2:54
Gladstone AsderGladstone Asder
5313921
$endgroup$
1
$begingroup$
You'll find some concrete illustration of how IVP and BVP behave differently in IVP vs. BVP
$endgroup$
– user147263
Jul 27 '14 at 4:46
add a comment |
$begingroup$
I don't really see the difference, because in both case we need to determine y and the values of the constants. The only difference is that we give the value of y and y' in the former and the value of either 2 y or 2 y' in the latter.
I solve both problems the same way. I don't really understand the theory, I guess.
ordinary-differential-equations
asked May 18 '13 at 2:54
Gladstone AsderGladstone Asder
5313921
$endgroup$
I don't really see the difference, because in both case we need to determine y and the values of the constants. The only difference is that we give the value of y and y' in the former and the value of either 2 y or 2 y' in the latter.
I solve both problems the same way. I don't really understand the theory, I guess.
ordinary-differential-equations
ordinary-differential-equations
asked May 18 '13 at 2:54
Gladstone AsderGladstone Asder
5313921
asked May 18 '13 at 2:54
Gladstone AsderGladstone Asder
5313921
asked May 18 '13 at 2:54
Gladstone AsderGladstone Asder
5313921
asked May 18 '13 at 2:54
Gladstone AsderGladstone Asder
5313921
asked May 18 '13 at 2:54
Gladstone AsderGladstone Asder
5313921
5313921
1
$begingroup$
You'll find some concrete illustration of how IVP and BVP behave differently in IVP vs. BVP
$endgroup$
– user147263
Jul 27 '14 at 4:46
add a comment |
1
$begingroup$
You'll find some concrete illustration of how IVP and BVP behave differently in IVP vs. BVP
$endgroup$
– user147263
Jul 27 '14 at 4:46
1
1
$begingroup$
You'll find some concrete illustration of how IVP and BVP behave differently in IVP vs. BVP
$endgroup$
– user147263
Jul 27 '14 at 4:46
$begingroup$
You'll find some concrete illustration of how IVP and BVP behave differently in IVP vs. BVP
$endgroup$
– user147263
Jul 27 '14 at 4:46
add a comment |
8 Answers
8
active
oldest
votes
$begingroup$
An initial value problem is how to aim my gun. A boundary value problem is how to aim my gun so that the bullet hits the target.
Qualitatively the methods of solution are sometimes different, because Taylor series approximate a function at a single point, i.e. at 0.
answered May 18 '13 at 3:12
vadim123vadim123
76.1k897190
$endgroup$
add a comment |
$begingroup$
For a simple example (second order ODE), an initial value problem would say $y(a)=p$, $y'(a)=q$.
A boundary value problem would specify $y(a)=p$, $y(b)=q$.
answered May 18 '13 at 3:04
André NicolasAndré Nicolas
453k36427813
$endgroup$
add a comment |
$begingroup$
Initial Value Problems:
In initial value problems, we are given the value of function $y(x)$ and its derivative $y'(x)$ at the same point ( initial point ) sy at $x = 0$
i.e $y(0)= xi1$ and $y'(0)= x_2$.
Boundary Value Problems:
In boundary value problem, we are given the value of function $y(x)$ at two different points, i.e $y(a)= x_1$ and $y(b)= x_2$.
edited Oct 4 '15 at 8:12
Scientifica
6,78641335
answered Oct 4 '15 at 7:53
Muhammad TariqMuhammad Tariq
311
$endgroup$
add a comment |
$begingroup$
Initial Value Problems:
Initial value problem does not require to specify the value at boundaries, instead it needs the value during initial condition. This usually apply for dynamic system that is changing over time as in Physics. An example, to solve a particle position under differential equation, we need the initial position and also initial velocity. Without these initial values, we cannot determine the final position from the equation.
Boundary Value Problems:
In contrast, boundary value problems not necessarily used for dynamic system. Instead, it is very useful for a system that has space boundary. An example would be shape from shading problem in computer vision. To determine surface gradient from the PDE, one should impose boundary values on the region of interest.
answered Oct 5 '15 at 7:25
habibhabib
211
$endgroup$
add a comment |
$begingroup$
Initial value problem will be given initial conditions. But the boundary value problem contains boundary conditions like y(x1) and y(x2).
answered May 28 '16 at 12:42
K S RupaK S Rupa
111
$endgroup$
add a comment |
$begingroup$
In initial value problem values are given according to initial stages such as when there is initial stage means at zero time the Velocity and Acceleration have zero values similarly in initial value problems the points given according to zero value of that function and its derivative.
Where in boundary value problem the end points are non zero element means at t>0 the conditions given will called the boundary value problems.
For Example.
G(0)=0 , G'(0)=0 I,C's (Initial conditions)
G(2)=4 , G'(1)=3 B,C's (Boundary conditions)
answered Apr 14 '17 at 19:18
Mirza Ali RazaMirza Ali Raza
1
$endgroup$
add a comment |
$begingroup$
Initial valye problems are those,which are related to the initial conditions of a question and no limit is used.
While boundry vaue problems are those in which limit is used i.e an interval is given !
answered Feb 28 '15 at 16:41
Mohammad shehryarMohammad shehryar
1
$endgroup$
add a comment |
$begingroup$
In initial value problem we always want to determine the value of f(x)and f'(x) at initial point it may be 0 or something else but initial like f(1)=3 and f'(1)=2 then we can determine the constant.But in boundry value problem the condition will in form of a interval i.e.f(0)=3,f(2)=5
answered Nov 25 '17 at 14:32
vasant kumar mishravasant kumar mishra
1
$endgroup$
$begingroup$
Welcome to MSE. What's the point of providing an answer to a question posted years ago and which has an accepted answer?
$endgroup$
– José Carlos Santos
Nov 25 '17 at 14:36
add a comment |
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8 Answers
8
active
oldest
votes
8 Answers
8
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
An initial value problem is how to aim my gun. A boundary value problem is how to aim my gun so that the bullet hits the target.
Qualitatively the methods of solution are sometimes different, because Taylor series approximate a function at a single point, i.e. at 0.
answered May 18 '13 at 3:12
vadim123vadim123
76.1k897190
$endgroup$
add a comment |
$begingroup$
An initial value problem is how to aim my gun. A boundary value problem is how to aim my gun so that the bullet hits the target.
Qualitatively the methods of solution are sometimes different, because Taylor series approximate a function at a single point, i.e. at 0.
answered May 18 '13 at 3:12
vadim123vadim123
76.1k897190
$endgroup$
add a comment |
$begingroup$
An initial value problem is how to aim my gun. A boundary value problem is how to aim my gun so that the bullet hits the target.
Qualitatively the methods of solution are sometimes different, because Taylor series approximate a function at a single point, i.e. at 0.
answered May 18 '13 at 3:12
vadim123vadim123
76.1k897190
$endgroup$
An initial value problem is how to aim my gun. A boundary value problem is how to aim my gun so that the bullet hits the target.
Qualitatively the methods of solution are sometimes different, because Taylor series approximate a function at a single point, i.e. at 0.
answered May 18 '13 at 3:12
vadim123vadim123
76.1k897190
answered May 18 '13 at 3:12
vadim123vadim123
76.1k897190
answered May 18 '13 at 3:12
vadim123vadim123
76.1k897190
answered May 18 '13 at 3:12
vadim123vadim123
76.1k897190
76.1k897190
add a comment |
add a comment |
$begingroup$
For a simple example (second order ODE), an initial value problem would say $y(a)=p$, $y'(a)=q$.
A boundary value problem would specify $y(a)=p$, $y(b)=q$.
answered May 18 '13 at 3:04
André NicolasAndré Nicolas
453k36427813
$endgroup$
add a comment |
$begingroup$
For a simple example (second order ODE), an initial value problem would say $y(a)=p$, $y'(a)=q$.
A boundary value problem would specify $y(a)=p$, $y(b)=q$.
answered May 18 '13 at 3:04
André NicolasAndré Nicolas
453k36427813
$endgroup$
add a comment |
$begingroup$
For a simple example (second order ODE), an initial value problem would say $y(a)=p$, $y'(a)=q$.
A boundary value problem would specify $y(a)=p$, $y(b)=q$.
answered May 18 '13 at 3:04
André NicolasAndré Nicolas
453k36427813
$endgroup$
For a simple example (second order ODE), an initial value problem would say $y(a)=p$, $y'(a)=q$.
A boundary value problem would specify $y(a)=p$, $y(b)=q$.
answered May 18 '13 at 3:04
André NicolasAndré Nicolas
453k36427813
answered May 18 '13 at 3:04
André NicolasAndré Nicolas
453k36427813
answered May 18 '13 at 3:04
André NicolasAndré Nicolas
453k36427813
answered May 18 '13 at 3:04
André NicolasAndré Nicolas
453k36427813
453k36427813
add a comment |
add a comment |
$begingroup$
Initial Value Problems:
In initial value problems, we are given the value of function $y(x)$ and its derivative $y'(x)$ at the same point ( initial point ) sy at $x = 0$
i.e $y(0)= xi1$ and $y'(0)= x_2$.
Boundary Value Problems:
In boundary value problem, we are given the value of function $y(x)$ at two different points, i.e $y(a)= x_1$ and $y(b)= x_2$.
edited Oct 4 '15 at 8:12
Scientifica
6,78641335
answered Oct 4 '15 at 7:53
Muhammad TariqMuhammad Tariq
311
$endgroup$
add a comment |
$begingroup$
Initial Value Problems:
In initial value problems, we are given the value of function $y(x)$ and its derivative $y'(x)$ at the same point ( initial point ) sy at $x = 0$
i.e $y(0)= xi1$ and $y'(0)= x_2$.
Boundary Value Problems:
In boundary value problem, we are given the value of function $y(x)$ at two different points, i.e $y(a)= x_1$ and $y(b)= x_2$.
edited Oct 4 '15 at 8:12
Scientifica
6,78641335
answered Oct 4 '15 at 7:53
Muhammad TariqMuhammad Tariq
311
$endgroup$
add a comment |
$begingroup$
Initial Value Problems:
In initial value problems, we are given the value of function $y(x)$ and its derivative $y'(x)$ at the same point ( initial point ) sy at $x = 0$
i.e $y(0)= xi1$ and $y'(0)= x_2$.
Boundary Value Problems:
In boundary value problem, we are given the value of function $y(x)$ at two different points, i.e $y(a)= x_1$ and $y(b)= x_2$.
edited Oct 4 '15 at 8:12
Scientifica
6,78641335
answered Oct 4 '15 at 7:53
Muhammad TariqMuhammad Tariq
311
$endgroup$
Initial Value Problems:
In initial value problems, we are given the value of function $y(x)$ and its derivative $y'(x)$ at the same point ( initial point ) sy at $x = 0$
i.e $y(0)= xi1$ and $y'(0)= x_2$.
Boundary Value Problems:
In boundary value problem, we are given the value of function $y(x)$ at two different points, i.e $y(a)= x_1$ and $y(b)= x_2$.
edited Oct 4 '15 at 8:12
Scientifica
6,78641335
answered Oct 4 '15 at 7:53
Muhammad TariqMuhammad Tariq
311
edited Oct 4 '15 at 8:12
Scientifica
6,78641335
edited Oct 4 '15 at 8:12
Scientifica
6,78641335
edited Oct 4 '15 at 8:12
Scientifica
6,78641335
6,78641335
answered Oct 4 '15 at 7:53
Muhammad TariqMuhammad Tariq
311
answered Oct 4 '15 at 7:53
Muhammad TariqMuhammad Tariq
311
answered Oct 4 '15 at 7:53
Muhammad TariqMuhammad Tariq
311
311
add a comment |
add a comment |
$begingroup$
Initial Value Problems:
Initial value problem does not require to specify the value at boundaries, instead it needs the value during initial condition. This usually apply for dynamic system that is changing over time as in Physics. An example, to solve a particle position under differential equation, we need the initial position and also initial velocity. Without these initial values, we cannot determine the final position from the equation.
Boundary Value Problems:
In contrast, boundary value problems not necessarily used for dynamic system. Instead, it is very useful for a system that has space boundary. An example would be shape from shading problem in computer vision. To determine surface gradient from the PDE, one should impose boundary values on the region of interest.
answered Oct 5 '15 at 7:25
habibhabib
211
$endgroup$
add a comment |
$begingroup$
Initial Value Problems:
Initial value problem does not require to specify the value at boundaries, instead it needs the value during initial condition. This usually apply for dynamic system that is changing over time as in Physics. An example, to solve a particle position under differential equation, we need the initial position and also initial velocity. Without these initial values, we cannot determine the final position from the equation.
Boundary Value Problems:
In contrast, boundary value problems not necessarily used for dynamic system. Instead, it is very useful for a system that has space boundary. An example would be shape from shading problem in computer vision. To determine surface gradient from the PDE, one should impose boundary values on the region of interest.
answered Oct 5 '15 at 7:25
habibhabib
211
$endgroup$
add a comment |
$begingroup$
Initial Value Problems:
Initial value problem does not require to specify the value at boundaries, instead it needs the value during initial condition. This usually apply for dynamic system that is changing over time as in Physics. An example, to solve a particle position under differential equation, we need the initial position and also initial velocity. Without these initial values, we cannot determine the final position from the equation.
Boundary Value Problems:
In contrast, boundary value problems not necessarily used for dynamic system. Instead, it is very useful for a system that has space boundary. An example would be shape from shading problem in computer vision. To determine surface gradient from the PDE, one should impose boundary values on the region of interest.
answered Oct 5 '15 at 7:25
habibhabib
211
$endgroup$
Initial Value Problems:
Initial value problem does not require to specify the value at boundaries, instead it needs the value during initial condition. This usually apply for dynamic system that is changing over time as in Physics. An example, to solve a particle position under differential equation, we need the initial position and also initial velocity. Without these initial values, we cannot determine the final position from the equation.
Boundary Value Problems:
In contrast, boundary value problems not necessarily used for dynamic system. Instead, it is very useful for a system that has space boundary. An example would be shape from shading problem in computer vision. To determine surface gradient from the PDE, one should impose boundary values on the region of interest.
answered Oct 5 '15 at 7:25
habibhabib
211
answered Oct 5 '15 at 7:25
habibhabib
211
answered Oct 5 '15 at 7:25
habibhabib
211
answered Oct 5 '15 at 7:25
habibhabib
211
211
add a comment |
add a comment |
$begingroup$
Initial value problem will be given initial conditions. But the boundary value problem contains boundary conditions like y(x1) and y(x2).
answered May 28 '16 at 12:42
K S RupaK S Rupa
111
$endgroup$
add a comment |
$begingroup$
Initial value problem will be given initial conditions. But the boundary value problem contains boundary conditions like y(x1) and y(x2).
answered May 28 '16 at 12:42
K S RupaK S Rupa
111
$endgroup$
add a comment |
$begingroup$
Initial value problem will be given initial conditions. But the boundary value problem contains boundary conditions like y(x1) and y(x2).
answered May 28 '16 at 12:42
K S RupaK S Rupa
111
$endgroup$
Initial value problem will be given initial conditions. But the boundary value problem contains boundary conditions like y(x1) and y(x2).
answered May 28 '16 at 12:42
K S RupaK S Rupa
111
answered May 28 '16 at 12:42
K S RupaK S Rupa
111
answered May 28 '16 at 12:42
K S RupaK S Rupa
111
answered May 28 '16 at 12:42
K S RupaK S Rupa
111
111
add a comment |
add a comment |
$begingroup$
In initial value problem values are given according to initial stages such as when there is initial stage means at zero time the Velocity and Acceleration have zero values similarly in initial value problems the points given according to zero value of that function and its derivative.
Where in boundary value problem the end points are non zero element means at t>0 the conditions given will called the boundary value problems.
For Example.
G(0)=0 , G'(0)=0 I,C's (Initial conditions)
G(2)=4 , G'(1)=3 B,C's (Boundary conditions)
answered Apr 14 '17 at 19:18
Mirza Ali RazaMirza Ali Raza
1
$endgroup$
add a comment |
$begingroup$
In initial value problem values are given according to initial stages such as when there is initial stage means at zero time the Velocity and Acceleration have zero values similarly in initial value problems the points given according to zero value of that function and its derivative.
Where in boundary value problem the end points are non zero element means at t>0 the conditions given will called the boundary value problems.
For Example.
G(0)=0 , G'(0)=0 I,C's (Initial conditions)
G(2)=4 , G'(1)=3 B,C's (Boundary conditions)
answered Apr 14 '17 at 19:18
Mirza Ali RazaMirza Ali Raza
1
$endgroup$
add a comment |
$begingroup$
In initial value problem values are given according to initial stages such as when there is initial stage means at zero time the Velocity and Acceleration have zero values similarly in initial value problems the points given according to zero value of that function and its derivative.
Where in boundary value problem the end points are non zero element means at t>0 the conditions given will called the boundary value problems.
For Example.
G(0)=0 , G'(0)=0 I,C's (Initial conditions)
G(2)=4 , G'(1)=3 B,C's (Boundary conditions)
answered Apr 14 '17 at 19:18
Mirza Ali RazaMirza Ali Raza
1
$endgroup$
In initial value problem values are given according to initial stages such as when there is initial stage means at zero time the Velocity and Acceleration have zero values similarly in initial value problems the points given according to zero value of that function and its derivative.
Where in boundary value problem the end points are non zero element means at t>0 the conditions given will called the boundary value problems.
For Example.
G(0)=0 , G'(0)=0 I,C's (Initial conditions)
G(2)=4 , G'(1)=3 B,C's (Boundary conditions)
answered Apr 14 '17 at 19:18
Mirza Ali RazaMirza Ali Raza
1
answered Apr 14 '17 at 19:18
Mirza Ali RazaMirza Ali Raza
1
answered Apr 14 '17 at 19:18
Mirza Ali RazaMirza Ali Raza
1
answered Apr 14 '17 at 19:18
Mirza Ali RazaMirza Ali Raza
1
1
add a comment |
add a comment |
$begingroup$
Initial valye problems are those,which are related to the initial conditions of a question and no limit is used.
While boundry vaue problems are those in which limit is used i.e an interval is given !
answered Feb 28 '15 at 16:41
Mohammad shehryarMohammad shehryar
1
$endgroup$
add a comment |
$begingroup$
Initial valye problems are those,which are related to the initial conditions of a question and no limit is used.
While boundry vaue problems are those in which limit is used i.e an interval is given !
answered Feb 28 '15 at 16:41
Mohammad shehryarMohammad shehryar
1
$endgroup$
add a comment |
$begingroup$
Initial valye problems are those,which are related to the initial conditions of a question and no limit is used.
While boundry vaue problems are those in which limit is used i.e an interval is given !
answered Feb 28 '15 at 16:41
Mohammad shehryarMohammad shehryar
1
$endgroup$
Initial valye problems are those,which are related to the initial conditions of a question and no limit is used.
While boundry vaue problems are those in which limit is used i.e an interval is given !
answered Feb 28 '15 at 16:41
Mohammad shehryarMohammad shehryar
1
answered Feb 28 '15 at 16:41
Mohammad shehryarMohammad shehryar
1
answered Feb 28 '15 at 16:41
Mohammad shehryarMohammad shehryar
1
answered Feb 28 '15 at 16:41
Mohammad shehryarMohammad shehryar
1
1
add a comment |
add a comment |
$begingroup$
In initial value problem we always want to determine the value of f(x)and f'(x) at initial point it may be 0 or something else but initial like f(1)=3 and f'(1)=2 then we can determine the constant.But in boundry value problem the condition will in form of a interval i.e.f(0)=3,f(2)=5
answered Nov 25 '17 at 14:32
vasant kumar mishravasant kumar mishra
1
$endgroup$
$begingroup$
Welcome to MSE. What's the point of providing an answer to a question posted years ago and which has an accepted answer?
$endgroup$
– José Carlos Santos
Nov 25 '17 at 14:36
add a comment |
$begingroup$
In initial value problem we always want to determine the value of f(x)and f'(x) at initial point it may be 0 or something else but initial like f(1)=3 and f'(1)=2 then we can determine the constant.But in boundry value problem the condition will in form of a interval i.e.f(0)=3,f(2)=5
answered Nov 25 '17 at 14:32
vasant kumar mishravasant kumar mishra
1
$endgroup$
$begingroup$
Welcome to MSE. What's the point of providing an answer to a question posted years ago and which has an accepted answer?
$endgroup$
– José Carlos Santos
Nov 25 '17 at 14:36
add a comment |
$begingroup$
In initial value problem we always want to determine the value of f(x)and f'(x) at initial point it may be 0 or something else but initial like f(1)=3 and f'(1)=2 then we can determine the constant.But in boundry value problem the condition will in form of a interval i.e.f(0)=3,f(2)=5
answered Nov 25 '17 at 14:32
vasant kumar mishravasant kumar mishra
1
$endgroup$
In initial value problem we always want to determine the value of f(x)and f'(x) at initial point it may be 0 or something else but initial like f(1)=3 and f'(1)=2 then we can determine the constant.But in boundry value problem the condition will in form of a interval i.e.f(0)=3,f(2)=5
answered Nov 25 '17 at 14:32
vasant kumar mishravasant kumar mishra
1
answered Nov 25 '17 at 14:32
vasant kumar mishravasant kumar mishra
1
answered Nov 25 '17 at 14:32
vasant kumar mishravasant kumar mishra
1
answered Nov 25 '17 at 14:32
vasant kumar mishravasant kumar mishra
1
1
$begingroup$
Welcome to MSE. What's the point of providing an answer to a question posted years ago and which has an accepted answer?
$endgroup$
– José Carlos Santos
Nov 25 '17 at 14:36
add a comment |
$begingroup$
Welcome to MSE. What's the point of providing an answer to a question posted years ago and which has an accepted answer?
$endgroup$
– José Carlos Santos
Nov 25 '17 at 14:36
$begingroup$
Welcome to MSE. What's the point of providing an answer to a question posted years ago and which has an accepted answer?
$endgroup$
– José Carlos Santos
Nov 25 '17 at 14:36
$begingroup$
Welcome to MSE. What's the point of providing an answer to a question posted years ago and which has an accepted answer?
$endgroup$
– José Carlos Santos
Nov 25 '17 at 14:36
add a comment |
Thanks for contributing an answer to Mathematics Stack Exchange!
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$begingroup$
You'll find some concrete illustration of how IVP and BVP behave differently in IVP vs. BVP
$endgroup$
– user147263
Jul 27 '14 at 4:46