Numerical Methods

  1. Partial Differential Equations
    1. PDE Classification
      1. Second-Order PDEs
        1. Elliptic Equations
          1. Laplace Equation
            1. Poisson Equation
              1. Boundary Conditions
              2. Parabolic Equations
                1. Heat Equation
                  1. Diffusion Equations
                    1. Initial and Boundary Conditions
                    2. Hyperbolic Equations
                      1. Wave Equation
                        1. Transport Equations
                          1. Characteristic Methods
                        2. Finite Difference Methods
                          1. Grid Generation
                            1. Uniform Grids
                              1. Nonuniform Grids
                                1. Boundary Conforming
                                2. Difference Approximations
                                  1. Central Differences
                                    1. Forward and Backward
                                      1. Higher-Order Schemes
                                      2. Elliptic Problems
                                        1. Five-Point Stencil
                                          1. Iterative Solution
                                            1. Multigrid Methods
                                            2. Parabolic Problems
                                              1. Explicit Schemes
                                                1. Implicit Schemes
                                                  1. Crank-Nicolson Method
                                                    1. Stability Analysis
                                                    2. Hyperbolic Problems
                                                      1. Upwind Schemes
                                                        1. Lax-Wendroff Method
                                                          1. CFL Condition
                                                        2. Finite Element Method Introduction
                                                          1. Weak Formulation
                                                            1. Variational Principles
                                                              1. Integration by Parts
                                                                1. Boundary Conditions
                                                                2. Element Types
                                                                  1. Linear Elements
                                                                    1. Quadratic Elements
                                                                      1. Shape Functions
                                                                      2. Assembly Process
                                                                        1. Element Matrices
                                                                          1. Global System
                                                                            1. Boundary Conditions
                                                                            2. Solution Techniques
                                                                              1. Direct Solvers
                                                                                1. Iterative Solvers

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                                                                            9. Ordinary Differential Equations

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                                                                            11. Optimization Methods