Mixing
ODE: Difference between explicit and implicit schemes
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I'm trying to prepare for my exam in ordinary differential equations and I've got this question. (Stiffness)
"fundamental difference between explicit and implicit schemes"
My own idea is that explicit method is based on previus calculations. I.e. Explicit Euler method. But how about Implicit Euler?
ordinary-differential-equations numerical-methods
edited Jan 11 at 15:21
LutzL
58k42054
asked Jan 11 at 13:18
Joey AdamsJoey Adams
457
$endgroup$
add a comment |
$begingroup$
I'm trying to prepare for my exam in ordinary differential equations and I've got this question. (Stiffness)
"fundamental difference between explicit and implicit schemes"
My own idea is that explicit method is based on previus calculations. I.e. Explicit Euler method. But how about Implicit Euler?
ordinary-differential-equations numerical-methods
edited Jan 11 at 15:21
LutzL
58k42054
asked Jan 11 at 13:18
Joey AdamsJoey Adams
457
$endgroup$
$begingroup$
Do you know how implicit Euler, the implicit trapezoidal method or 2-stage Gauß work? What the equations are, what is trivial, what is non-trivial about them? What a predictor-corrector scheme is and how simplified Newton might give a slight advantage?
$endgroup$
– LutzL
Jan 11 at 13:24
add a comment |
$begingroup$
I'm trying to prepare for my exam in ordinary differential equations and I've got this question. (Stiffness)
"fundamental difference between explicit and implicit schemes"
My own idea is that explicit method is based on previus calculations. I.e. Explicit Euler method. But how about Implicit Euler?
ordinary-differential-equations numerical-methods
edited Jan 11 at 15:21
LutzL
58k42054
asked Jan 11 at 13:18
Joey AdamsJoey Adams
457
$endgroup$
I'm trying to prepare for my exam in ordinary differential equations and I've got this question. (Stiffness)
"fundamental difference between explicit and implicit schemes"
My own idea is that explicit method is based on previus calculations. I.e. Explicit Euler method. But how about Implicit Euler?
ordinary-differential-equations numerical-methods
ordinary-differential-equations numerical-methods
edited Jan 11 at 15:21
LutzL
58k42054
asked Jan 11 at 13:18
Joey AdamsJoey Adams
457
edited Jan 11 at 15:21
LutzL
58k42054
asked Jan 11 at 13:18
Joey AdamsJoey Adams
457
edited Jan 11 at 15:21
LutzL
58k42054
edited Jan 11 at 15:21
LutzL
58k42054
edited Jan 11 at 15:21
LutzL
58k42054
58k42054
asked Jan 11 at 13:18
Joey AdamsJoey Adams
457
asked Jan 11 at 13:18
Joey AdamsJoey Adams
457
asked Jan 11 at 13:18
Joey AdamsJoey Adams
457
457
$begingroup$
Do you know how implicit Euler, the implicit trapezoidal method or 2-stage Gauß work? What the equations are, what is trivial, what is non-trivial about them? What a predictor-corrector scheme is and how simplified Newton might give a slight advantage?
$endgroup$
– LutzL
Jan 11 at 13:24
add a comment |
$begingroup$
Do you know how implicit Euler, the implicit trapezoidal method or 2-stage Gauß work? What the equations are, what is trivial, what is non-trivial about them? What a predictor-corrector scheme is and how simplified Newton might give a slight advantage?
$endgroup$
– LutzL
Jan 11 at 13:24
$begingroup$
Do you know how implicit Euler, the implicit trapezoidal method or 2-stage Gauß work? What the equations are, what is trivial, what is non-trivial about them? What a predictor-corrector scheme is and how simplified Newton might give a slight advantage?
$endgroup$
– LutzL
Jan 11 at 13:24
$begingroup$
Do you know how implicit Euler, the implicit trapezoidal method or 2-stage Gauß work? What the equations are, what is trivial, what is non-trivial about them? What a predictor-corrector scheme is and how simplified Newton might give a slight advantage?
$endgroup$
– LutzL
Jan 11 at 13:24
add a comment |
1 Answer
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Implicit schemes are implicit, that is, you have to solve a non-linear equation or at least approximate the solution better than the discretization error.
Explicit methods are never A-stable, implicit methods can be A-stable, some even satisfy more specialized stability conditions. Stability is important for solving stiff equations, as it allows larger step sizes.
answered Jan 11 at 13:27
LutzLLutzL
58k42054
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add a comment |
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1 Answer
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active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
Implicit schemes are implicit, that is, you have to solve a non-linear equation or at least approximate the solution better than the discretization error.
Explicit methods are never A-stable, implicit methods can be A-stable, some even satisfy more specialized stability conditions. Stability is important for solving stiff equations, as it allows larger step sizes.
answered Jan 11 at 13:27
LutzLLutzL
58k42054
$endgroup$
add a comment |
$begingroup$
Implicit schemes are implicit, that is, you have to solve a non-linear equation or at least approximate the solution better than the discretization error.
Explicit methods are never A-stable, implicit methods can be A-stable, some even satisfy more specialized stability conditions. Stability is important for solving stiff equations, as it allows larger step sizes.
answered Jan 11 at 13:27
LutzLLutzL
58k42054
$endgroup$
add a comment |
$begingroup$
Implicit schemes are implicit, that is, you have to solve a non-linear equation or at least approximate the solution better than the discretization error.
Explicit methods are never A-stable, implicit methods can be A-stable, some even satisfy more specialized stability conditions. Stability is important for solving stiff equations, as it allows larger step sizes.
answered Jan 11 at 13:27
LutzLLutzL
58k42054
$endgroup$
Implicit schemes are implicit, that is, you have to solve a non-linear equation or at least approximate the solution better than the discretization error.
Explicit methods are never A-stable, implicit methods can be A-stable, some even satisfy more specialized stability conditions. Stability is important for solving stiff equations, as it allows larger step sizes.
answered Jan 11 at 13:27
LutzLLutzL
58k42054
answered Jan 11 at 13:27
LutzLLutzL
58k42054
answered Jan 11 at 13:27
LutzLLutzL
58k42054
answered Jan 11 at 13:27
LutzLLutzL
58k42054
58k42054
add a comment |
add a comment |
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Do you know how implicit Euler, the implicit trapezoidal method or 2-stage Gauß work? What the equations are, what is trivial, what is non-trivial about them? What a predictor-corrector scheme is and how simplified Newton might give a slight advantage?
$endgroup$
– LutzL
Jan 11 at 13:24