Question

In: Advanced Math

Consider the following first-order ODE dy/dx=x^2/y from x = 0 to x = 2.4 with y(0)...

Consider the following first-order ODE dy/dx=x^2/y from x = 0 to x = 2.4 with y(0) = 2. (a) solving with Euler’s explicit method using h = 0.6 (b) solving with midpoint method using h = 0.6 (c) solving with classical fourth-order Runge-Kutta method using h = 0.6. Plot the x-y curve according to your solution for both (a) and (b).

Solutions

Expert Solution

n Xn Yn K1 K2
0 0 2 0 0.0270
1 0.6 2.0270 0.1066 0.2336
2 1.2 2.2606 0.3822 0.5506
3 1.8 2.8113 0.6915 0.8381
4 2.4 3.6494 0.9470 1.0609

n Xn Yn K1 K2 K3 K4
0 0 2 0 0.0270 0.0268 0.1066
1 0.6 2.0357 0.106106 0.2327 0.2258 0.3820
2 1.2 2.2699 0.380634 0.5487 0.5306 0.6942
3 1.8 2.8088 0.692109 0.8387 0.8197 0.9525
4 2.4 3.6357 0.950575 1.0640 1.0495 1.1526

d)


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