HW_09 - nonlinear boundary value problem. . 1 ) 1 ( ) ( 1 ,...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
ChE 348 Homework # 9 _______________________________________________________________________ _ 1. Use a finite difference method (based on central differences) with a mesh size h = 0.25 to solve (by hand) the boundary value problem. . 2 ) 1 ( ) 0 ( 1 0 , ) 1 ( // = = = - + - y y x x y x y 2. Write a computer program that approximates the solutions of the linear boundary value problem . 1 ) ( ) 0 ( 1 0 , ) 3 cos 5 ( 2 // = = - = - pi y y x x y x y Using a finite difference method (based on central differences) with a sequence of grids, h = π /8, π /16, and π /32. Do the approximate solutions appear to be converging to a solution? 3. Use a shooting method combined with Euler’s method to solve (by hand) the
Background image of page 1
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: nonlinear boundary value problem. . 1 ) 1 ( ) ( 1 , 2 // = = = +-y y x x y y Show the first three iterations with a mesh size of h = 0.5. 4. Consider the nonlinear boundary value problem . 3 ) 2 ( , ) ( 2 , // = = = +-y y x x e y y Use the shooting method combined with the trapezoid rule predictor-corrector to construct solutions to this equation, and then use a forth-order Runge-Kutta scheme and compare the two approximate solutions. Are they nearly the same? Use a mesh size of h = 0.2....
View Full Document

Ask a homework question - tutors are online