Mixing
Iteration algorithm for finding better approximation in Shooting method for solving BVP
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Good day, everyone. Basically , the problem I am given is to solve the system of differential equations with 4 equations, and I have two initial values, and two boundary conditions. Following the Shooting method theory, I supply my system with two guesses for missing initial values, solve the system using Runge-Kutta 4th order, and obtain some values for functions, which are not right based on my boundary conditions.The question is how to iterate my system of approximations for initial values, to obtain right initial guesses? If I had only one value to be found by this method, it would be easy, by just implementing some form of linear interpolation, squeezing down the solution from two ends. But since there are two values guessed, it is not working anymore. Any ideas would be greatly appreciated.
numerical-methods runge-kutta-methods
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Farid Hasanov
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Good day, everyone. Basically , the problem I am given is to solve the system of differential equations with 4 equations, and I have two initial values, and two boundary conditions. Following the Shooting method theory, I supply my system with two guesses for missing initial values, solve the system using Runge-Kutta 4th order, and obtain some values for functions, which are not right based on my boundary conditions.The question is how to iterate my system of approximations for initial values, to obtain right initial guesses? If I had only one value to be found by this method, it would be easy, by just implementing some form of linear interpolation, squeezing down the solution from two ends. But since there are two values guessed, it is not working anymore. Any ideas would be greatly appreciated.
numerical-methods runge-kutta-methods
asked yesterday
Farid Hasanov
1
New contributor
Farid Hasanov is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
My functions are like this: $dot x_1(t) = x_2(t)$, $dot x_2(t) = p_2(t)-sqrt 2 x_1(t)e^{-alpha t}$, $dot p_1(t) = sqrt 2 p_2(t)e^{-alpha t}+x_1(t)$, $dot p_2(t) = -p_1(t)$ with initial and boundary values of: $x_1(0)=1,p_2(0)=0 p_1(1)=0,p_2(1)=0$
– Farid Hasanov
23 hours ago
add a comment |
up vote
0
down vote
favorite
up vote
0
down vote
favorite
Good day, everyone. Basically , the problem I am given is to solve the system of differential equations with 4 equations, and I have two initial values, and two boundary conditions. Following the Shooting method theory, I supply my system with two guesses for missing initial values, solve the system using Runge-Kutta 4th order, and obtain some values for functions, which are not right based on my boundary conditions.The question is how to iterate my system of approximations for initial values, to obtain right initial guesses? If I had only one value to be found by this method, it would be easy, by just implementing some form of linear interpolation, squeezing down the solution from two ends. But since there are two values guessed, it is not working anymore. Any ideas would be greatly appreciated.
numerical-methods runge-kutta-methods
asked yesterday
Farid Hasanov
1
New contributor
Farid Hasanov is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
Good day, everyone. Basically , the problem I am given is to solve the system of differential equations with 4 equations, and I have two initial values, and two boundary conditions. Following the Shooting method theory, I supply my system with two guesses for missing initial values, solve the system using Runge-Kutta 4th order, and obtain some values for functions, which are not right based on my boundary conditions.The question is how to iterate my system of approximations for initial values, to obtain right initial guesses? If I had only one value to be found by this method, it would be easy, by just implementing some form of linear interpolation, squeezing down the solution from two ends. But since there are two values guessed, it is not working anymore. Any ideas would be greatly appreciated.
numerical-methods runge-kutta-methods
numerical-methods runge-kutta-methods
asked yesterday
Farid Hasanov
1
New contributor
Farid Hasanov is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked yesterday
Farid Hasanov
1
New contributor
Farid Hasanov is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked yesterday
Farid Hasanov
1
New contributor
Farid Hasanov is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked yesterday
Farid Hasanov
1
asked yesterday
Farid Hasanov
1
1
New contributor
Farid Hasanov is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
New contributor
Farid Hasanov is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
Farid Hasanov is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
My functions are like this: $dot x_1(t) = x_2(t)$, $dot x_2(t) = p_2(t)-sqrt 2 x_1(t)e^{-alpha t}$, $dot p_1(t) = sqrt 2 p_2(t)e^{-alpha t}+x_1(t)$, $dot p_2(t) = -p_1(t)$ with initial and boundary values of: $x_1(0)=1,p_2(0)=0 p_1(1)=0,p_2(1)=0$
– Farid Hasanov
23 hours ago
add a comment |
My functions are like this: $dot x_1(t) = x_2(t)$, $dot x_2(t) = p_2(t)-sqrt 2 x_1(t)e^{-alpha t}$, $dot p_1(t) = sqrt 2 p_2(t)e^{-alpha t}+x_1(t)$, $dot p_2(t) = -p_1(t)$ with initial and boundary values of: $x_1(0)=1,p_2(0)=0 p_1(1)=0,p_2(1)=0$
– Farid Hasanov
23 hours ago
My functions are like this: $dot x_1(t) = x_2(t)$, $dot x_2(t) = p_2(t)-sqrt 2 x_1(t)e^{-alpha t}$, $dot p_1(t) = sqrt 2 p_2(t)e^{-alpha t}+x_1(t)$, $dot p_2(t) = -p_1(t)$ with initial and boundary values of: $x_1(0)=1,p_2(0)=0 p_1(1)=0,p_2(1)=0$
– Farid Hasanov
23 hours ago
My functions are like this: $dot x_1(t) = x_2(t)$, $dot x_2(t) = p_2(t)-sqrt 2 x_1(t)e^{-alpha t}$, $dot p_1(t) = sqrt 2 p_2(t)e^{-alpha t}+x_1(t)$, $dot p_2(t) = -p_1(t)$ with initial and boundary values of: $x_1(0)=1,p_2(0)=0 p_1(1)=0,p_2(1)=0$
– Farid Hasanov
23 hours ago
add a comment |
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Farid Hasanov is a new contributor. Be nice, and check out our Code of Conduct.
Farid Hasanov is a new contributor. Be nice, and check out our Code of Conduct.
Farid Hasanov is a new contributor. Be nice, and check out our Code of Conduct.
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My functions are like this: $dot x_1(t) = x_2(t)$, $dot x_2(t) = p_2(t)-sqrt 2 x_1(t)e^{-alpha t}$, $dot p_1(t) = sqrt 2 p_2(t)e^{-alpha t}+x_1(t)$, $dot p_2(t) = -p_1(t)$ with initial and boundary values of: $x_1(0)=1,p_2(0)=0 p_1(1)=0,p_2(1)=0$
– Farid Hasanov
23 hours ago