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7. (15pts) Consider the two-point boundary value problem u" + 2xu' x²u = x², u(0) = 1, u(1) = 0. - (a) Let h=1/4. Write out the difference equations explicitely, using centered-difference quotients for all derivatives. (b) Convert the equations to a linear system Ax = b, and then solve the system (either by hand or using MATLAB).

7. (15pts) Consider the two-point boundary value problem u" + 2xu' x²u = x², u(0) = 1, u(1) = 0. - (a) Let h=1/4. Write out the difference equations explicitely, using centered-difference quotients for all derivatives. (b) Convert the equations to a linear system Ax = b, and then solve the system (either by hand or using MATLAB).

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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7. (15pts) Consider the two-point boundary value problem u" + 2xu' x²u = x², u(0) = 1, u(1) = 0. - (a) Let h=1/4. Write out the difference equations explicitely, using centered-difference quotients for all derivatives. (b) Convert the equations to a linear system Ax = b, and then solve the system (either by hand or using MATLAB).
Transcribed Image Text:7. (15pts) Consider the two-point boundary value problem u" + 2xu' x²u = x², u(0) = 1, u(1) = 0. - (a) Let h=1/4. Write out the difference equations explicitely, using centered-difference quotients for all derivatives. (b) Convert the equations to a linear system Ax = b, and then solve the system (either by hand or using MATLAB).
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