Numerical Methods for Engineers
Numerical Methods for Engineers
7th Edition
ISBN: 9780073397924
Author: Steven C. Chapra Dr., Raymond P. Canale
Publisher: McGraw-Hill Education
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Chapter 30, Problem 15P

Solve the following PDE:

2 u x 2 + b u x = u t

Boundary conditions u ( 0 , t ) = 0 u ( 1 , t ) = 0
Initial conditions u ( x , 0 ) = 0 0 x 1

Use second-order accurate finite-difference analogues for the derivatives with a Crank-

Nicolson formulation to integrate in time. Write a computer program for the solution.

Increase the value of Δ t by 10% for each time step to more quickly obtain the steady-

state solution, and select values of Δ t and Δ t for good accuracy. Plot u versus x for various values of t. Solve for values of b = 5   4 ,   2 ,   0 ,   2 ,   4 .

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