MATH 573 ASSIGNMENT 91. LetY=wzandF(x, Y) =f1(x, w, z)f2(x, w, z). Heun’s method for the system of differentialequationsY=F(x, Y), with initial conditionY(x0) =Y0, is given by:Yn+1=Yn+h2F(xn, Yn) +h2F(xn+h, Yn+hF(xn, Yn)).Find approximations tow(h) andz(h) for the systemw=z,z=-cw,w(0) =a,z(0) =b,wherea, b, care given constants.2. Consider the approximation of the initial value problemy=f(x, y),y(x0) =y0,by a class of explicit linear multistep methods of the form:yn+1=a0yn+a1yn-1+h[b0fn+b1fn-1].If the constanta0is considered fixed, determine values of the constants
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