Numerical analysis Math Problem Example | Topics and Well Written Essays - 1500 words

Numerical analysis - Math Problem ExampleThis method of numerical integration finds solutions in the form of ensuant solutions.The equation given in the task was solved by Mathcad program using program module which allows to solve differential equations with fixed step F = rkfixed(Z0, t0, tk, N, f). The result of the solution of this equation in mathcad is the followingIn order to evaluate these results we can solve the same equation using conventional means. As its shown this equation is solved by the method of variables separation. After finding the function we should plug the set of t into this function and find its values for all values of t on the interval 0,1. As we can see the results of numerical solution of Runge Kutta method are very close to the real results of this function.Using misapprehension evaluation methodAbsolute value (real value of function- approximated value)/ real value of function) we will get the following resultsReal values00.10.20.30.40.50.60.70.80.911 1.0050131.0202011.0460281.0832871.1331481.1972171.2776211.3771281.4993031.648721Errors01.25E-050.0001972.66E-050.0002650.0001310.0001820.00039.28E-050.0002020.00017As we can see the results are very reliable as error is less than 0.001% for all values