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1. Show that the 2nd order difference equation (2) for 0²U 8² U 0x² ôt² = t> 0, U(x,0) = f(x), Ut(x,0) = g(x) (1) is consistent as an approximation to (1) 878 where for example, Uij = U ij so that with r = h/k U₁j+1 = r²U₁−1j + 2(1 − r²)Uij + r²Ui+1j — Uij-1 87 wij = Wi.j+1 - 2Wij + Wi.j-1; Wij = w(xi, tj)

1. Show that the 2nd order difference equation (2) for 0²U 8² U 0x² ôt² = t> 0, U(x,0) = f(x), Ut(x,0) = g(x) (1) is consistent as an approximation to (1) 878 where for example, Uij = U ij so that with r = h/k U₁j+1 = r²U₁−1j + 2(1 − r²)Uij + r²Ui+1j — Uij-1 87 wij = Wi.j+1 - 2Wij + Wi.j-1; Wij = w(xi, tj)

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. Show that the 2nd order difference equation (2) for U U 827 = 827 t> 0, is consistent as an approximation to (1) = h² so that with r = h/k = Ujj+1 -dzuij U(x,0) = f(x), Ut(x,0) = g(x) where for example, :r²Ui–1j + 2(1 − r²)Uij + r²Ui+¹j — Uij-1 87 wij (1) = Wi.j+1 −2Wij + Wi.j-1; Wij = : w(xi, tj)
Transcribed Image Text:1. Show that the 2nd order difference equation (2) for U U 827 = 827 t> 0, is consistent as an approximation to (1) = h² so that with r = h/k = Ujj+1 -dzuij U(x,0) = f(x), Ut(x,0) = g(x) where for example, :r²Ui–1j + 2(1 − r²)Uij + r²Ui+¹j — Uij-1 87 wij (1) = Wi.j+1 −2Wij + Wi.j-1; Wij = : w(xi, tj)
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