Purchase Solution

Numerical Integration and the Runge Kutta Method

Not what you're looking for?

Ask Custom Question

a) For a fixed delta t(i+1)= delta t, the linear equation, x = Ax, x(t0)=x0 has the solution... Show that the Runge Kutta method (below) is 3rd order and not 4th order for the above linear equation.

bi) Find the exact solution of x = -2x, x0 = 3
bii) Find the numerical solution for two simulation steps using explicit Euler and delta t=0.2.
biii) Find the numerical solution for two simulation steps using modified Euler and delta t=0.2.
biv) Find the global error at t=0.4 for the above methods. What do you expect will happen to these errors if the step size is halved?

See the attached file.

Attachments
Purchase this Solution
Solution Summary

This solution is provided in 718 words combined and attached in two separate .doc files. It uses step-by-step equations for solving the mathematical problems regarding the numerical integration and uses the Runge Kutta method.

Purchase this Solution
Free BrainMass Quizzes
Architectural History

This quiz is intended to test the basics of History of Architecture- foundation for all architectural courses.

Air Pollution Control - Environmental Science

Working principle of ESP

View More Free Quizzes
Related BrainMass Solutions

  • Matlab: Runge-Kutta versus Euler in a Lottka-Volterra example

    Plot the phase curves. How the results compare with the curves obtained using the Runge-Kutta method? An example of a Matlab script to calculate and plot the three solutions on the same plot is attached.

  • Euler, Improved Euler, and Runge Kutta for Lorenz attractor, and Butterfly Effect

    The solution helps implement the Euler integration scheme and the Runge-Kutta integration scheme for various equations.

  • Numerical solutions Euler & Runge Kutta

    Compare the solutions for the approximation (linear) and numerical(non-linear) using the numerical method runge kutta of 4th DEGREE OR HIGHER(preferrably 4th-6th order). Please include the following details: 1.

  • Numerical Integration

    It is then compared with the Runge-Kutta Method

  • Runge-Kutta, Lorenz Attractor, Butterfly Effect

    In a Matlab script, we demonstrate the application of the Runge-Kutta numerical method for a Lorenz attractor, the Butterfly Effect caused by a small change of initial conditions, and the dependence of the Butterfly Effect on the step of the integration

  • Runge-Kutta 4

    The solution shows in a step by step manner how to solve a first order differential equation using order 4 Runge-Kutta method and comparing it to the analytic solution

  • Initial-Value Problem : Euler and Runge-Kutta Method

    30846 Initial-Value Problem : Euler and Runge-Kutta Method Solve the following initial value problem by Euler's method using h = 0.1. Find an error by comparing to exact solution. Then solve it by the Runge-Kutta method. Find an error.

  • Explicit Runge-Kutta Method

    If anything is in the least unclear, please ask you questions via messages and I shall do my best to explain. The solution writes the general purpose of Runge-Kutta method. A description is provided in matlab.

  • Runge-Kutta Method

    548485 Runge-Kutta Method Problem 1 1. Write an Matlab m-file to solve this problem with Runge-Kutta method. Solve the concentration of T1 and T2 (or salt content) as function of time (up to 100 minutes).

View More Related Solutions