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.

Operations Research : Applications and Algorithms

4th Edition

ISBN:9780534380588

Author:Wayne L. Winston

Publisher:Wayne L. Winston

Chapter2: Basic Linear Algebra

Section2.2: Matrices And Systems Of Linear Equations

Problem 1P

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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].
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