Theory of Initial Value Problems

Theory of Initial Value Problems (Part II)

Nonlinear Equations. Fixed Point Technique for Scalar Equations

Nonlinear Systems of Equations. Fixed Point Technique

Newton Method for Scalar Equations

Newton Method for Nonlinear Systems

Broyden and Steepest Descent Methods for Nonlinear Systems

Linear Shooting Method for ODE BVPs

Nonlinear Shooting Method for ODE BVPs

Finite-Difference Methods for Linear BVPs

Finite-Difference Methods for Linear BVPs with Neumann boundary Conditions

Finite-Difference Methods for Nonlinear BVPs

Derivation of Finite Difference Approximations

More on Finite Difference Approximation

Partial Differential Equations: Elliptic Equations

Partial Differential Equations: Parabolic Equations

Matrix Norms

Matrix Stability

Application of Matrix Stability: Heat Conduction

Finite-Difference Methods for Parabolic Equations with two space variables

Tridiagonal Algorithm (Crout)