9.7Matrix Method for Stability9.8Derivative Boundary Conditions9.9Hyperbolic Equations9.9.1StabilityProblems1. Use a von Neumann stability analysis to show for the wave equation that a simple explicitEuler predictor using central diFerencing in space is unstable. The diFerence equation isun+1j=unj−c∆t∆axunj+1−unj−12!Now show that the same diFerence method is stable when written as the implicit formulaun+1j=unj−c∆t∆xun+1j+1−un+1j−12!2. Prove that the C±L condition is the stability requirement when the Lax WendroF methodis applied to solve the simple 1-D wave equation. The diFerence equation is of the form:un+1j=unj−c∆t2∆xunj+1−un
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