(a) Construct a third-order accurate Lax-wendroff-type method for the advection equation in the following way: *...

 

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(a) Construct a third-order accurate Lax-wendroff-type method for the advection equation in the following way: * + * Expand u(x,t+k) in a Taylor series and keep the first four terms. Replace all time derivatives by spatial derivatives using the advection equation. Construct a cubic polynomial passing through the points U 1-2, Up1 Up, and Up+1 - Approximate the spatial derivatives in the Taylor series by the exact derivatives of the above constructed cubic polynomial. (b) Verify that the trucation is O (K) if h = O(k). (c) Determine the stability restriction on k for this method. (a) Construct a third-order accurate Lax-wendroff-type method for the advection equation in the following way: * + * Expand u(x,t+k) in a Taylor series and keep the first four terms. Replace all time derivatives by spatial derivatives using the advection equation. Construct a cubic polynomial passing through the points U 1-2, Up1 Up, and Up+1 - Approximate the spatial derivatives in the Taylor series by the exact derivatives of the above constructed cubic polynomial. (b) Verify that the trucation is O (K) if h = O(k). (c) Determine the stability restriction on k for this method.

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a The thirdorder accurate LaxWendrofftype method for the advection equation can be constructed as fo... View the full answer