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1. Solve the following second-order ordinary differential equation using fourth-order Runge-Kutta method with the step size h=0.5: +0.6 +8y=0 dy dx The initial values are y(x=0) = 4, y (x=0)=0. Calculate the solution at x=1. The analytical solution is given by y(x) d'y dz2 = 4e-0.3 sin(2.81247x) +0.426671e-0.3 "cos(2.81247x) Report the solution and the true relative global error in % for each step. Show all computational steps.

1. Solve the following second-order ordinary differential equation using fourth-order Runge-Kutta method with the step size h=0.5: +0.6 +8y=0 dy dx The initial values are y(x=0) = 4, y (x=0)=0. Calculate the solution at x=1. The analytical solution is given by y(x) d'y dz2 = 4e-0.3 sin(2.81247x) +0.426671e-0.3 "cos(2.81247x) Report the solution and the true relative global error in % for each step. Show all computational steps.

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter11: Differential Equations
Section11.CR: Chapter 11 Review
Problem 33CR
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1. Solve the following second-order ordinary differential equation using fourth-order Runge-Kutta method with the step size h=0.5: d'y dx² dy +0.6- +8y=0 dx dy The initial values are y(x=0) = 4, (x=0)=0. Calculate the solution at x = 1. dx The analytical solution is given by y (x) = 4e 0.3 sin(2.81247x) +0.426671e-0.3 cos (2.81247x) Report the solution and the true relative global error in % for each step. Show all computational steps.
Transcribed Image Text:1. Solve the following second-order ordinary differential equation using fourth-order Runge-Kutta method with the step size h=0.5: d'y dx² dy +0.6- +8y=0 dx dy The initial values are y(x=0) = 4, (x=0)=0. Calculate the solution at x = 1. dx The analytical solution is given by y (x) = 4e 0.3 sin(2.81247x) +0.426671e-0.3 cos (2.81247x) Report the solution and the true relative global error in % for each step. Show all computational steps.
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