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13 changes: 3 additions & 10 deletions
13
Math-ODE.package/ExplicitStepper.class/instance/doStep.time.stepSize..st
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| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -1,13 +1,6 @@ | ||
| stepping | ||
| doStep: aState time: t stepSize: dt | ||
| doStep: aState time: t stepSize: timeStep | ||
| "This method should take one step from inState at time t of size dt, and modify the state, then answer it. The default implementation here is Euler Method. Subclasses should override" | ||
| | dxdt | | ||
| dxdt := system x: aState t: t. | ||
| aState isNumber | ||
| ifTrue: [^ (dt * dxdt + aState)] | ||
| ifFalse: | ||
| [(1 to aState size) | ||
| do: [:i | | xi | | ||
| xi := aState at: i. | ||
| aState at: i put: (dxdt at: i) * dt + xi]. | ||
| ^ aState.] | ||
| self stepSize: timeStep. | ||
| ^ self doStep: aState time: t. |
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| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -0,0 +1,3 @@ | ||
| A RungeKuttaStepper is a specialization on Explicit Stepper that provides a higer order estimate. The Euler method implemented in ExplicitStepper is order 1, and the error obtained is proportional to the step size. | ||
|
|
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| The RungeKuttaStepper is order 4, the error term is proportional to the step size to the fourth power. |
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| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -0,0 +1,4 @@ | ||
| accessing | ||
| order | ||
| "RungeKutta is a fourth order method." | ||
| ^ 4 |
13 changes: 13 additions & 0 deletions
13
Math-ODE.package/RungeKuttaStepper.class/instance/collectionDoStep.time..st
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| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -0,0 +1,13 @@ | ||
| stepping | ||
| collectionDoStep: aState time: t | ||
| "aState is a collection/vector, and system is a vector function. Take a single step using fourth order runge-kutta." | ||
| | k1 k2 k3 k4 midPoint endPoint| | ||
| midPoint := self stepSize / 2 + t. | ||
| endPoint := self stepSize + t. | ||
| k1 := system x: aState t: t. | ||
| k2 := system x: aState + (k1 * self stepSize / 2) t: midPoint. | ||
| k3 := system x: aState + (k2 * self stepSize / 2 ) t: midPoint. | ||
| k4 := system x: aState + (k3 * self stepSize) t: endPoint. | ||
| Transcript show: t; show: aState; cr. | ||
| ^ aState + ((k1 + k2 + k2 + k3 + k3 + k4) / 6 * self stepSize). | ||
|
|
10 changes: 10 additions & 0 deletions
10
Math-ODE.package/RungeKuttaStepper.class/instance/doStep.time..st
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| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -0,0 +1,10 @@ | ||
| stepping | ||
| doStep: aState time: t | ||
| "This method should take one step from inState at time t of size dt, and modify the state, then answer it." | ||
| self stepSize isNil ifTrue: [self error: 'step size required by stepper']. | ||
| aState isNumber | ||
| ifTrue: | ||
| [^ (self numberDoStep: aState time: t)] | ||
| "a collection" | ||
| ifFalse: | ||
| [^ (self collectionDoStep: aState time: t)] |
9 changes: 9 additions & 0 deletions
9
Math-ODE.package/RungeKuttaStepper.class/instance/numberDoStep.time..st
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| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -0,0 +1,9 @@ | ||
| stepping | ||
| numberDoStep: aState time: t | ||
| "state is a number. Take a single step at t." | ||
| | k1 k2 k3 k4 | | ||
| k1 := system x: aState t: t. | ||
| k2 := system x: aState + (k1 * self stepSize / 2 ) t: self stepSize / 2 + t. | ||
| k3 := system x: aState + (k2 * self stepSize / 2 ) t: self stepSize / 2 + t. | ||
| k4 := system x: aState + (self stepSize * k3) t: self stepSize + t. | ||
| ^ aState + ((k1 + k2 + k2 + k3 + k3 + k4)/ 6 * self stepSize). |
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| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -0,0 +1,16 @@ | ||
| { | ||
| "category" : "Math-ODE", | ||
| "classinstvars" : [ | ||
| ], | ||
| "classtraitcomposition" : "{}", | ||
| "classvars" : [ | ||
| ], | ||
| "commentStamp" : "<historical>", | ||
| "instvars" : [ | ||
| ], | ||
| "name" : "RungeKuttaStepper", | ||
| "pools" : [ | ||
| ], | ||
| "super" : "ExplicitStepper", | ||
| "traitcomposition" : "{}", | ||
| "type" : "normal" } |
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| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -1,2 +1 @@ | ||
| SystemOrganization addCategory: #'Math-ODE'! | ||
| SystemOrganization addCategory: #'Math-ODE-Tests'! |
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Empty file.
9 changes: 9 additions & 0 deletions
9
Math-ODETests.package/RungeKuttaStepperTest.class/instance/testSimpleSystem.st
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| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -0,0 +1,9 @@ | ||
| as yet unclassified | ||
| testSimpleSystem | ||
| | solver stepper system dt | | ||
| dt := 0.01. | ||
| system := ExplicitSystem block: [:x :t | t sin]. | ||
| stepper := RungeKuttaStepper onSystem: system. | ||
| solver := (ODESolver new) stepper: stepper; system: system; dt: dt. | ||
| self should: [(solver solve: system startState: -1 startTime: 0 endTime: Float pi) closeTo: 1]. | ||
|
|
12 changes: 12 additions & 0 deletions
12
Math-ODETests.package/RungeKuttaStepperTest.class/instance/testVectorSystem.st
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| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -0,0 +1,12 @@ | ||
| as yet unclassified | ||
| testVectorSystem | ||
| | solver stepper system dt | | ||
| dt := 0.01. | ||
| system := ExplicitSystem block: [:x :t | | c | c:= DhbVector new: 2. | ||
| c at: 1 put: t sin. | ||
| c at: 2 put: t cos. | ||
| c]. | ||
| stepper := RungeKuttaStepper onSystem: system. | ||
| solver := (ODESolver new) stepper: stepper; system: system; dt: dt. | ||
| self should: [((solver solve: system startState: #(-1 0) startTime: 0 endTime: Float pi ) at: 1)closeTo: 1]. | ||
| self should: [((solver solve: system startState: #(-1 0) startTime: 0 endTime: Float pi / 2 ) at: 2 ) closeTo: 1]. |
16 changes: 16 additions & 0 deletions
16
Math-ODETests.package/RungeKuttaStepperTest.class/properties.json
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| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -0,0 +1,16 @@ | ||
| { | ||
| "category" : "Math-ODETests", | ||
| "classinstvars" : [ | ||
| ], | ||
| "classtraitcomposition" : "{}", | ||
| "classvars" : [ | ||
| ], | ||
| "commentStamp" : "", | ||
| "instvars" : [ | ||
| ], | ||
| "name" : "RungeKuttaStepperTest", | ||
| "pools" : [ | ||
| ], | ||
| "super" : "TestCase", | ||
| "traitcomposition" : "{}", | ||
| "type" : "normal" } |
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