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Use the difference equation U+12+1, + 2(1-x²)uy + X²u,-1,-₁,-1 to approximate the solution of the boundary-value problem 20²u 0²u dx² 01² u(0, t) = 0, u(a, t) = 0, 0≤stsT อน at u(x, 0) = f(x), for the given cases. (Give the approximations obtained for t= T. Round your answers to four decimal places.). (a) c=1, a=1, T-1, f(x)= x(1-x); n = 4 and m - 20 u(0.25, 1) u(0.50, 1) u(0.75, 1) (c) (b) c-1, a-2, T-1, f(x)=e-18(x-1)2; n = 5 and m - 10 u(0.4, 1) u(0.8, 1) u(1.2, 1) u(1.6, 1) , 0

Use the difference equation U+12+1, + 2(1-x²)uy + X²u,-1,-₁,-1 to approximate the solution of the boundary-value problem 20²u 0²u dx² 01² u(0, t) = 0, u(a, t) = 0, 0≤stsT อน at u(x, 0) = f(x), for the given cases. (Give the approximations obtained for t= T. Round your answers to four decimal places.). (a) c=1, a=1, T-1, f(x)= x(1-x); n = 4 and m - 20 u(0.25, 1) u(0.50, 1) u(0.75, 1) (c) (b) c-1, a-2, T-1, f(x)=e-18(x-1)2; n = 5 and m - 10 u(0.4, 1) u(0.8, 1) u(1.2, 1) u(1.6, 1) , 0

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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Use the difference equation U₁+1=²+1, +2(12²)uj + X²u₁-1,-₁,-1 to approximate the solution of the boundary-value problem 202ud²u गर 0<x<a, 0 <t<T ax² u(0, t) = 0, u(a, t) = 0, 0 st≤T u(x, 0) = f(x), อน at t=0 for the given cases. (Give the approximations obtained for t= T. Round your answers to four decimal places.) (a) c=1, a = 1, T = 1, f(x)= x(1-x); n = 4 and m = 20 u(0.25, 1) = u(0.50, 1) u(0.75, 1) = 0, 0sxsa, (b) c=1, a=2, T=1, f(x)=e-18(x-1)²; n = 5 and m = 10 u(0.4, 1) = u(0.8, 1) = u(1.2, 1) = u(1.6, 1) u(0.1, 1) u(0.2, 1) = u(0.3, 1) u(0.4, 1) = u(0.5, 1) (c) c=√√√2. a-1, T = 1, f(x) = (0, u(0.6, 1) u(0.7, 1)) u(0.8, 1) = u(0.9, 1) = n 10 and m = 25 0≤x≤ 0.5 10.8, 0.5<x< 1;
Transcribed Image Text:Use the difference equation U₁+1=²+1, +2(12²)uj + X²u₁-1,-₁,-1 to approximate the solution of the boundary-value problem 202ud²u गर 0<x<a, 0 <t<T ax² u(0, t) = 0, u(a, t) = 0, 0 st≤T u(x, 0) = f(x), อน at t=0 for the given cases. (Give the approximations obtained for t= T. Round your answers to four decimal places.) (a) c=1, a = 1, T = 1, f(x)= x(1-x); n = 4 and m = 20 u(0.25, 1) = u(0.50, 1) u(0.75, 1) = 0, 0sxsa, (b) c=1, a=2, T=1, f(x)=e-18(x-1)²; n = 5 and m = 10 u(0.4, 1) = u(0.8, 1) = u(1.2, 1) = u(1.6, 1) u(0.1, 1) u(0.2, 1) = u(0.3, 1) u(0.4, 1) = u(0.5, 1) (c) c=√√√2. a-1, T = 1, f(x) = (0, u(0.6, 1) u(0.7, 1)) u(0.8, 1) = u(0.9, 1) = n 10 and m = 25 0≤x≤ 0.5 10.8, 0.5<x< 1;
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