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These are questions asked by alshehri

(a) Design your own 3-stage explicit Runge-Kutta method with one-step error O(h4).

(b) Test your method by solving y= −y. Confirm that the global error in your numerical solution

is O(h3).

Write a Maple procedure that solves for y(1) in the initial value problem

                     y= f(y),     y(0) = 1,



using a numerical stencil based on the nth order Taylor series expansion of y. The procedure’s arguments should include an arbitrary function f, an integer n representing the accuracy of the Taylor series expansion, another integer N representing the number of steps between x = 0 and x = 1. Pick a test problem and compare your results with the output of dsolve/numeric.



this question about midpoint method I need help with the part c



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