The question is to find interval of absolute stability for third order Taylor series Method to souve IBVP y = xy y/no)=yo 2h ( 4²8 x + = + ²x + 4x + 1) = 4?f z Y z X (4×)7 for stability (EX(h) |
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- xy" + x(1 + x)y' – 3(3+ x)y = 0 Use the appropriate method to determine two linearly independent series solutions about x, = 0. Indicate, the indicial equation, the root(s) of the indicial equation, and the recurrence relation, where applicable. Determine its second series solution using Wronskian Method. By substitute e^-x as a seriesUse Taylor series terms from zero to fourth order to approximatethe function: f(x) = x4− 3x2+5x-1 Since xi = 0.8 with h = 1. That is, predict the value of the function at xi+1 = 1.8with the Taylor Series of first, second, third and fourth order.express f(x+h)=cos(x+h) in terms of x and h (step size) using the first 5 terms of taylor series. Show complete solution.
- (a) Find the power series solution of y′′ − 2xy ′ + y = 0 about the ordinary point x = 0. (b) Is there any singular point of the DE? What is the interval of convergence of your power series solution?1.Using zero, first, second, and third order Taylor series, estimate the function at the point xi+1 = 0.5 based on the function value xi = 0. 2.Using the half interval method, find the intersection between the curves y = ex and y = 3x by looking for the root of 3x – 3x2 = 0. The calculation accuracy is 0.5%,Given that the taylor series at 0 for 1/(1-x)= 1+x+x2+x3+x4+....+xn+... a) Find the taylor series at 0 for 1/(1-8x3) b) find its interval of convergence