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2-Calculate a finite-difference solution of the equation OU OU êt dx² U = 0 when t=0 for 0≤x≤ 1/ satisfying the initial condition and the boundary condition au ax = =0 at x=0 and 00, au ax 1 at x = - for 1>0, 1 i) Using an explicit method with dx=0.1 and r=- 4 ii) Using the Crank-Nikolson equations with 6x=0.1 for two time-steps. and r= 1 for two time-steps.

2-Calculate a finite-difference solution of the equation OU OU êt dx² U = 0 when t=0 for 0≤x≤ 1/ satisfying the initial condition and the boundary condition au ax = =0 at x=0 and 00, au ax 1 at x = - for 1>0, 1 i) Using an explicit method with dx=0.1 and r=- 4 ii) Using the Crank-Nikolson equations with 6x=0.1 for two time-steps. and r= 1 for two time-steps.

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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2-Calculate a finite-difference solution of the equation OU OU êt dx² satisfying the initial condition and the boundary condition au ax = 0<x< , 1>0, =0 at x = 0 and U=0 when t=0 for 0≤x≤ ·0sxs-12. au ax 1 at x = - for 1>0, 1 i) Using an explicit method with dx=0.1 and r=- 4 ii) Using the Crank-Nikolson equations with 6x=0.1 and r=1 for two time-steps. for two time-steps.
Transcribed Image Text:2-Calculate a finite-difference solution of the equation OU OU êt dx² satisfying the initial condition and the boundary condition au ax = 0<x< , 1>0, =0 at x = 0 and U=0 when t=0 for 0≤x≤ ·0sxs-12. au ax 1 at x = - for 1>0, 1 i) Using an explicit method with dx=0.1 and r=- 4 ii) Using the Crank-Nikolson equations with 6x=0.1 and r=1 for two time-steps. for two time-steps.
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