a) Solve the following system of equations using the Crank-Nicolson method ordinary differentials, for the first...
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a) Solve the following system of equations using the Crank-Nicolson method ordinary differentials, for the first two steps in t using At = 0.1 du, dt =12u₁ +4u₂ + 6te ¹²; u₁(0)=1 du, du₂ -3- =6u, +9u; u₂ (0)=-1 dt dt 2- b) Determines the order of the local error associated with a method that leads to the following one-step formula ₁+1= 12-62h+2²h² 12+62h+2²h² by discretizing the following ordinary differential equation: du =-Au, u(0)=uo. dt Check your result by applying the method to the case where λ = 0.5, u, = 100 and h = 11 40'80 a) Solve the following system of equations using the Crank-Nicolson method ordinary differentials, for the first two steps in t using At = 0.1 du, dt =12u₁ +4u₂ + 6te ¹²; u₁(0)=1 du, du₂ -3- =6u, +9u; u₂ (0)=-1 dt dt 2- b) Determines the order of the local error associated with a method that leads to the following one-step formula ₁+1= 12-62h+2²h² 12+62h+2²h² by discretizing the following ordinary differential equation: du =-Au, u(0)=uo. dt Check your result by applying the method to the case where λ = 0.5, u, = 100 and h = 11 40'80
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Related Book For
A Survey of Mathematics with Applications
ISBN: 978-0134112107
10th edition
Authors: Allen R. Angel, Christine D. Abbott, Dennis Runde
Posted Date:
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