Runge-Kutta method: Difference between revisions
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m Improve formatting of problem (\delta t not dt, \times not *) |
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{{draft task}} |
{{draft task}} |
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Given the example Differential equation: |
Given the example Differential equation: |
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:<math>y' = t \times \sqrt y</math> |
:<math>y'(t) = t \times \sqrt {y(t)}</math> |
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With initial condition: |
With initial condition: |
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:<math>t_0 = 0</math> and <math>y_0 = y(t_0) = y(0) = 1</math> |
:<math>t_0 = 0</math> and <math>y_0 = y(t_0) = y(0) = 1</math> |
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This equation has an exact solution: |
This equation has an exact solution: |
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:<math>y = \tfrac{1}{16}(t^2 +4)^2</math> |
:<math>y(t) = \tfrac{1}{16}(t^2 +4)^2</math> |
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;Task |
;Task |
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Demonstrate the commonly used explicit fourth-order Runge–Kutta method as defined in the [[wp:Runge–Kutta_methods#Common_fourth-order_Runge.E2.80.93Kutta_method|Wikipedia article]] to solve the above differential equation. |
Demonstrate the commonly used explicit fourth-order Runge–Kutta method as defined in the [[wp:Runge–Kutta_methods#Common_fourth-order_Runge.E2.80.93Kutta_method|Wikipedia article]] to solve the above differential equation. |
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