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# Solved: Use the Forward-Difference method to approximate the solution to the following

ISBN: 9780534392000 331

## Solution for problem 12.2.6 Chapter 12-2

Numerical Analysis (Available Titles CengageNOW) | 8th Edition

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Problem 12.2.6

Use the Forward-Difference method to approximate the solution to the following parabolic partial differential equations. a. u t 4 2 2u x 2 = 0, 0 < x < 4, 0 < t; u(0, t) = u(4, t) = 0, 0 < t, u(x, 0) = sin(x/4)(1 + 2 cos(x/4)), 0 x 4. Use h = 0.2 and k = 0.04, and compare your results at t = 0.4 to the actual solution u(x, t) = et sin(x/2) + et/4 sin(x/4). b. u t 1 2 2u x 2 = 0, 0 < x < 1, 0 < t; u(0, t) = u(1, t) = 0, 0 < t, u(x, 0) = cos x 1 2 , 0 x 1. Use h = 0.1 and k = 0.04, and compare your results at t = 0.4 to the actual solution u(x, t) = et cos (x 1 2 ).

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##### ISBN: 9780534392000

The answer to “Use the Forward-Difference method to approximate the solution to the following parabolic partial differential equations. a. u t 4 2 2u x 2 = 0, 0 < x < 4, 0 < t; u(0, t) = u(4, t) = 0, 0 < t, u(x, 0) = sin(x/4)(1 + 2 cos(x/4)), 0 x 4. Use h = 0.2 and k = 0.04, and compare your results at t = 0.4 to the actual solution u(x, t) = et sin(x/2) + et/4 sin(x/4). b. u t 1 2 2u x 2 = 0, 0 < x < 1, 0 < t; u(0, t) = u(1, t) = 0, 0 < t, u(x, 0) = cos x 1 2 , 0 x 1. Use h = 0.1 and k = 0.04, and compare your results at t = 0.4 to the actual solution u(x, t) = et cos (x 1 2 ).” is broken down into a number of easy to follow steps, and 149 words. This textbook survival guide was created for the textbook: Numerical Analysis (Available Titles CengageNOW) , edition: 8. Numerical Analysis (Available Titles CengageNOW) was written by and is associated to the ISBN: 9780534392000. The full step-by-step solution to problem: 12.2.6 from chapter: 12-2 was answered by , our top Calculus solution expert on 03/05/18, 08:28PM. Since the solution to 12.2.6 from 12-2 chapter was answered, more than 218 students have viewed the full step-by-step answer. This full solution covers the following key subjects: . This expansive textbook survival guide covers 69 chapters, and 1072 solutions.

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