[Solved] Following Forth Order Runge Kutta Method Commonly Used Mathematical Software Wo Yo J 1 2 3 Q37290503

The following is a forth-order Runge-Kutta method commonly used in mathematical software: wo Yo and for j-1, 2, 3, …, n-1 m-h f(tj, wj), m2ht+2, w,+ m), 2 WjW(m+2 m2+2ms+ma). 1. Write a Module that implements this forth-order Runge-Kutta method. Your Module should look similar to the above Heun’s method. Put comments in the Module similar to those in Heun’s method. You may discuss your work with others, but do not plagiarize others. 2. For the following iVP: y ‘-Exp[t] * Cos[y], y(0-0, use the forth- order Runge-Kutta method to approximate the solution on the interval 0st s4, using n 4, 8, 16, 32. Graph each approximation separately along with the direction field for this IVP. What can be said about this approximation method as the number of subintervals increases (step size decreases). Use your Show transcribed image text The following is a forth-order Runge-Kutta method commonly used in mathematical software: wo Yo and for j-1, 2, 3, …, n-1 m-h f(tj, wj), m2ht+2, w,+ m), 2 WjW(m+2 m2+2ms+ma). 1. Write a Module that implements this forth-order Runge-Kutta method. Your Module should look similar to the above Heun’s method. Put comments in the Module similar to those in Heun’s method. You may discuss your work with others, but do not plagiarize others. 2. For the following iVP: y ‘-Exp[t] * Cos[y], y(0-0, use the forth- order Runge-Kutta method to approximate the solution on the interval 0st s4, using n 4, 8, 16, 32. Graph each approximation separately along with the direction field for this IVP. What can be said about this approximation method as the number of subintervals increases (step size decreases). Use your

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Answer to The following is a forth-order Runge-Kutta method commonly used in mathematical software: wo Yo and for j-1, 2, 3, …, … . . .