Example: Differential Equations
The following example demonstrates how to use the Runge-Kutta program.
Example
Find the solution for the equation:
Y′′ = e2x at Xf = 1 with the initial conditions X0 = 0, Y(0) = 1, Y′(0) = 2, and a step size of 0.2.
This second-order equation reduces to the first-order equations y1′ = y2 and y2′ = e2x. The initial conditions become y1(0) = 1 and y2(0) = 2.
Procedure |
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| Enter the functions. | [ LEARN ] { 1st } [ 2nd ] [ LBL ] [ 2nd ] f 1 [ RCL ] M [ 2nd ] [ RTN ] [ 2nd ] LBL [ 2nd ] f 2 [ ( ] 2 [ x ] [ RCL ] E [ ) ] [ INV ] [ LN ] [ 2nd ] [ RTN ] [ LEARN ] |
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| Select the program | [ RUN ] { MTH } { --> } { R-K } |
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| Enter number of functions | 2 { n } |  |
| Enter the step size | .2 { h } |  |
| Enter initial value of x | 0 { LOx } |  |
| Enter ending value of x | 1 { HIx } |  |
| Proceed with program | { EOD } |  |
| Enter the initial y values | 1 { ENT } |  |
| 2 { ENT } |  |
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| Proceed with results | { NO } |  |
| Choose only the end results | { YES } |  |
| { NXT } |  |
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| { NXT } |  |
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The solution for y′′ is the value of y2.
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