Using Python: Solve the following equation numerically using the forward Euler method (du)/(dt)=t^(2)-10 with the initial condition u(0)=50 As part of the solution process converge the solution by decreasing the step size You can determine the solution by taking the root-mean-square of the error with respect to the exact solution. You will need to calculate the solution to this differential equation. Then for each step size h, you can calculate the root-mean-square of the error. Once the root-mean-square of the error is less than the accuracy of the solution, your result is converged. Choose a time grid say from 0 to 20. Once you have this working, try solving using the Forward Euler method, (du)/(dt)=u*cos(t) with the initial condition u(0)=1, and using a mesh from 0,10.

Using Python: Solve the following equation numerically using the forward Euler method (du)/(dt)=t^(2)-10 with the initial condition u(0)=50 As part of the solution process converge the solution by decreasing the step size You can determine the solution by taking the root-mean-square of the error with respect to the exact solution. You will need to calculate the solution to this differential equation. Then for each step size h, you can calculate the root-mean-square of the error. Once the root-mean-square of the error is less than the accuracy of the solution, your result is converged. Choose a time grid say from 0 to 20. Once you have this working, try solving using the Forward Euler method, (du)/(dt)=u*cos(t) with the initial condition u(0)=1, and using a mesh from 0,10.

C++ for Engineers and Scientists

4th Edition

ISBN:9781133187844

Author:Bronson, Gary J.

Publisher:Bronson, Gary J.

Chapter5: Repetition Statements

Section5.7: Do While Loops

Problem 6E: (Numerical analysis) Here’s a challenging problem for those who know a little calculus. The...

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