Consider the second-order boundary value problem y′′ +(2x^2 +3)y′ −y =6x, 0≤x ≤1, (4) y(0) =...

Consider the second-order boundary value problem

y′′ +(2x^2 +3)y′ −y =6x, 0≤x ≤1, (4)

y(0) = 1, y(1) = 0.
(a) Rewrite the second-order equation (4) as a system of two first-order equations

involving variables y and z. [2]

(b) Suppose that yn and zn are approximations to y(xn) and z(xn), respectively, where xn = nh, n = 0,...,N and h = 1/N for some positive integer N. Find the iterative formula when using the modified Euler method to approximate (4) with the modified boundary conditions:

y(0) = 1, y′(0) = z0.
(c) Hence, employ the shooting method, with underlying modified Euler method, to

find approximations yn, n = 1, . . . , N to problem (4)-(5), when N = 5. [Hint: Notice that differential equation (4) is linear.]

Expert Solution

Colby Messinger answered 5 months ago

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