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Solve the following equation numerically using the forward Euler method du =t²-10 with the initial condition u(0)=50 dt 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].

Solve the following equation numerically using the forward Euler method du =t²-10 with the initial condition u(0)=50 dt 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
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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Solve the following equation numerically using the forward Euler method du =t²-10 with the initial condition u(0)=50 dt 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].
Transcribed Image Text:Solve the following equation numerically using the forward Euler method du =t²-10 with the initial condition u(0)=50 dt 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].
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