Gauss Seidel method solves linear systems in diagonally dominant form. Also known as Liebmann method or successive displacement. Formula: x^(k+1) = L*^-1(b-Uxk)
Numerical methods find approximations to solutions of ordinary differential equations. First-order differential equations are Initial Value Problems. Picard-Lindelöf theorem guarantees unique solutions for Lipschitz-continuous functions
Iterative method for solving linear equations named after Gauss and Seidel. Convergence guaranteed only for strictly diagonally dominant or symmetric matrices. Method was first mentioned by Gauss in 1823, published by Seidel in 1874
FDMs solve differential equations by approximating derivatives with finite differences. Domain is discretized into intervals for numerical approximation. Modern computers efficiently perform linear algebra computations
Finds approximate solutions of first-order differential equations using Euler's method. Includes step-by-step solutions for better understanding. Requires input of differential equation, initial conditions, and step size
Simpson's Rule approximates integrals using quadratic polynomial approximations. Named after mathematician Thomas Simpson, it extends trapezoidal rule. Divides interval into smaller sections and fits parabolic curves