Consider the coupled system of second order differential equations subject to a(0) 1, a(1) 2, b(0) 0 and b(1) 1 Define a single system of unknowns y a 1 , b 1 , a 2 , b 2 , to solve this system by finite differences You do not need to convert this into an autonomous system of equations Determine th...

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Consider the coupled system of second-order differential equations subject to a(0) = 1, a(1) = 2, b(0)

Question:

Consider the coupled system of second-order differential equations 201 B' = xa- 2

subject to a(0) = 1, a′(1) = 2, b′(0) = 0 and b(1) = 1. Define a single system of unknowns y = [a₁, b₁, a₂, b₂, . . .] to solve this system by finite differences. You do not need to convert this into an autonomous system of equations. Determine the residuals (in terms of the unknowns yi) for n = 4 nodes.