[SOLVED] CSE218-ODE

Description

Solve the following ODE numerically from x=0 to x=10.

𝑑𝑦

= (𝑥 + 20𝑦) 𝑠𝑖𝑛(𝑥𝑦)

𝑑𝑥

Initial condition: y(0)=4

Apply Euler method, Heun’s method (with a single corrector), Midpoint method, Ralston’s method, and 4^th order RK method (as described in the book) to solve it. Write a single function for the 2^nd order RK method and pass the value of a₂ to the function for implementing Heun’s method, Midpoint method and Ralston’s method.

Use the following step sizes: 0.01, 0.05, 0.1, 0.5

Generate the following graphs from the (x,y) points you get.

• For each method, plot curves for all the step sizes in one graph (total 5 graphs, 4 curves in each graph)
• For each step size, plot curves for all the methods in one graph (total 4 graphs. 5 curves in each graph)

Proper labeling should be done in every graph.