Central difference numerical gradients can be used when solving differential equations using the finite difference method. The approach is important for numerically solving many engineering equations. An example of an ordinary differential equation (ODE) which represents a boundary value problem, where y is known at x = 2 and x = 4, is given below: dx + 4dv + 5y = 2x^3 dx^2 dx y(2) = 1, y(4) = 15. (a) Using a step size of h = 0.4, find the values of the matrix A and vector € in the matrix equation below, which can be formed when using central difference approximations to solve the boundary value equation (where Y1, Y2, Y3, J are the 4 unknown values of y). Show your working in full.
Ay = 0
2 2
2
€