Predictor-Corrector and Runge Kutta MethodsĬhapter 23. Ordinary Differential Equation - Initial Value Problems
Numerical Differentiation Problem Statementįinite Difference Approximating DerivativesĪpproximating of Higher Order DerivativesĬhapter 22. Least Square Regression for Nonlinear Functions Least Squares Regression Derivation (Multivariable Calculus) Least Squares Regression Derivation (Linear Algebra) Least Squares Regression Problem Statement Solve Systems of Linear Equations in PythonĮigenvalues and Eigenvectors Problem Statement Linear Algebra and Systems of Linear Equations Errors, Good Programming Practices, and DebuggingĬhapter 14. Inheritance, Encapsulation and PolymorphismĬhapter 10. Variables and Basic Data StructuresĬhapter 7. This code was originally written for Jacobi, and I provided the modification for making it into Gauss-Seidel.Python Programming And Numerical Methods: A Guide For Engineers And ScientistsĬhapter 2.
If you want, there is another way to calculate Jacobi and Gauss-Seidel, and you can take a look at that post here: Jacobi iteration doesn't end. Once we pass this point, then we use the variables calculated from the current iteration from the first variable up to the point where we are calculating, then use the rest of the variables for calculating the solution. If we are working on calculating the first variable, then we don't have any new information yet, and so we simply just update the solution using all of the previous information from the previous iteration. If idx = 1 %// Case where we are solving for the first variable Therefore: function z=gaussseidel(A,B) %// Change the function name This has to be done in the while loop, because that's where you're doing the iterations. For Gauss-Seidel, for each variable that you solve for, you must use the solutions of the previous variables calculated from the current iteration as part of the solution for the variable you are focusing on.Īs such, for your particular version of the code (though not optimal.), you simply need to add in a for loop where we solve for each variable one at a time, then keep feeding this information into the other variables. For Jacobi, you are simply using the previous iteration's solution to formulate the current solution.
, x_) as part of the solution for the current variable x_i. The difference between a Jacobi solver and a Gauss-Seidel solver is that when you're solving for the solution of a variable x_i at the current iteration, you need to use the information from the previous variables ( x_1, x_2.
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