d2y dx Consider the following ODE (boundary value problem) +64y = 0, 0x1, (x) ='(0) =...

 

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d2y dx² Consider the following ODE (boundary value problem) +64y = 0, 0≤x≤1, (x) ='(0) = 0 and y(1)=-1. хо In the method of finite differences, the derivatives are approximated by difference equations and the differential equation thus transforms into a system of equations. Using centered finite- difference formulas that are 2nd-order accurate and a set of n = 4 nodes of spacing h= 0.25, transform the ODE into a system of equations that can be solved to obtain the values of yo. Y₁. Y2, and y3 at these nodes. Express the resulting system of equations in matrix notation. Do NOT solve the system of equations. d2y dx² Consider the following ODE (boundary value problem) +64y = 0, 0≤x≤1, (x) ='(0) = 0 and y(1)=-1. хо In the method of finite differences, the derivatives are approximated by difference equations and the differential equation thus transforms into a system of equations. Using centered finite- difference formulas that are 2nd-order accurate and a set of n = 4 nodes of spacing h= 0.25, transform the ODE into a system of equations that can be solved to obtain the values of yo. Y₁. Y2, and y3 at these nodes. Express the resulting system of equations in matrix notation. Do NOT solve the system of equations.

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