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Solve the following differential equation using the finite-difference method. d²x(t) dt² + x(t) = 0 with specified initial conditions x(0) = 1 *(0) = 0

Solve the following differential equation using the finite-difference method. d²x(t) dt² + x(t) = 0 with specified initial conditions x(0) = 1 *(0) = 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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1. Solve the following differential equation using the finite-difference method. dx(t) + x(t) = 0 dt² with specified initial conditions x(0) = 1 *(0) = 0 The results obtained from the above exercise are summarized in the tabulation below, with comparison to the exact solution of x(t) = cos t. Variable, t Solution by the finite-difference method Exact solution % Error ANS 1 1 0.05 1 0.999 996 О.10 0.9975 0.995 0041 0.25 0.15 0.9925 0.988 77 0.38 0.20 0.9850 0.980 066 0.503
Transcribed Image Text:1. Solve the following differential equation using the finite-difference method. dx(t) + x(t) = 0 dt² with specified initial conditions x(0) = 1 *(0) = 0 The results obtained from the above exercise are summarized in the tabulation below, with comparison to the exact solution of x(t) = cos t. Variable, t Solution by the finite-difference method Exact solution % Error ANS 1 1 0.05 1 0.999 996 О.10 0.9975 0.995 0041 0.25 0.15 0.9925 0.988 77 0.38 0.20 0.9850 0.980 066 0.503
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