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Consider the following BVP for a second-order ODE: d'y = y+ sin x, 0sr<2, dx y(0) = 1.0, y(2) = 3.0. x in radian. (1) Using the central difference formula for approximating the second derivative, discretize the ODE to a finite difference equation. (a) If the step size is h=04, formulate the system of linear algebraic equations for the solution at the grid points and put it into the matrix form.

Consider the following BVP for a second-order ODE: d'y = y+ sin x, 0sr<2, dx y(0) = 1.0, y(2) = 3.0. x in radian. (1) Using the central difference formula for approximating the second derivative, discretize the ODE to a finite difference equation. (a) If the step size is h=04, formulate the system of linear algebraic equations for the solution at the grid points and put it into the matrix form.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Consider the following BVP for a second-order ODE: d'y dx = y+sin x , 0<xS 2, y(0) = 1.0, y(2) = 3.0. x in radian. (1) Using the central difference formula for approximating the second derivative, discretize the ODE to a finite difference equation. (a) If the step size is h=0.4, formulate the system of linear algebraic equations for the solution at the grid points and put it into the matrix form.
Transcribed Image Text:Consider the following BVP for a second-order ODE: d'y dx = y+sin x , 0<xS 2, y(0) = 1.0, y(2) = 3.0. x in radian. (1) Using the central difference formula for approximating the second derivative, discretize the ODE to a finite difference equation. (a) If the step size is h=0.4, formulate the system of linear algebraic equations for the solution at the grid points and put it into the matrix form.
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