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4. The Forward-Difference method for solving ut = a²uxx is Uį,j+1 = (1 − 2λ)U¡‚j + λ[Ui+1,j + Ui−1,j]. Now modify this to write out a formula for approximate the parabolic partial differential equation ut = a²uxx + F(x), 0 0. a² At Still use λ = in your formula. (Δx)2

4. The Forward-Difference method for solving ut = a²uxx is Uį,j+1 = (1 − 2λ)U¡‚j + λ[Ui+1,j + Ui−1,j]. Now modify this to write out a formula for approximate the parabolic partial differential equation ut = a²uxx + F(x), 0 0. a² At Still use λ = in your formula. (Δx)2

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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¡s Ui₁j+1 a²uxx ¡s Uį,j+1 = (1 − 2A)U¡‚j + A[Ui+1‚j + Ui-1,j]. 2λ)Uį,j Now modify this to write out a formula for approximate the parabolic partial differential equation ut = a²uxx + F(x), Ut 0 < x <l, t > 0. 4. The Forward-Difference method for solving ut = a²uxx Still use λ = a² At (Ax)² in your formula.
Transcribed Image Text:¡s Ui₁j+1 a²uxx ¡s Uį,j+1 = (1 − 2A)U¡‚j + A[Ui+1‚j + Ui-1,j]. 2λ)Uį,j Now modify this to write out a formula for approximate the parabolic partial differential equation ut = a²uxx + F(x), Ut 0 < x <l, t > 0. 4. The Forward-Difference method for solving ut = a²uxx Still use λ = a² At (Ax)² in your formula.
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