Consider the linear advection equation ut + aux = 0. Discretise this equation by the finite difference method, using an explicit Euler discretisation for the ast time derivative, and an upwind discretisation for the space derivative. At what value of the Courant number = - do we have a stable solution with 4x no dispersion and maximum diffusion errors? Give your answer to one decimal place.

Consider the linear advection equation ut + aux = 0. Discretise this equation by the finite difference method, using an explicit Euler discretisation for the ast time derivative, and an upwind discretisation for the space derivative. At what value of the Courant number = - do we have a stable solution with 4x no dispersion and maximum diffusion errors? Give your answer to one decimal place.

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter14: Discrete Dynamical Systems

Section14.3: Determining Stability

Problem 13E: Repeat the instruction of Exercise 11 for the function. f(x)=x3+x For part d, use i. a1=0.1 ii...

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