Unformatted text preview: 1 ) ( , 4 1 ) ( , 4 2 2 1 / 2 1 2 1 / 1== = += y y y y y y y y Compute out to x = 1.0, using the Trapezoidal rule predictorcorrector method. 5. Consider the secondorder equation ) ( , 8 1 ) ( , sin / // = = = + y y y y π ; write this as a firstorder system and compute (by hand) approximate solutions using a step size of h = π /10 and the Euler method. Show the first two steps. 6. Write a computer program that approximates the solution to the third order equation ; 3 ) ( , 1 ) ( , 1 ) ( , 8 10 2 2 5 4 // / 2 / // /// == = + + = + + + y y y x x y y y y using the following methods with h = 0.1 over the interval [0, 2]: (a) fourthorder RungeKutta (RK4) (b) Adams fourthorder predictor (AB4) and corrector (AM4) method with RK4 Compare the results with the true solution: 2 ) ( x e x y x + =...
View
Full Document
 Spring '08
 Chelikowsky
 Numerical Analysis, Heun's method, Runge–Kutta methods, Numerical ordinary differential equations

Click to edit the document details