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Numerical methods for physics

Alejandro L. Garcia

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Abstract

1. Preliminaries. 2. Ordinary Differential Equations I: Basic Methods. 3. Ordinary Differential Equations II: Advanced Methods. 4. Solving Systems of Equations. 5. Analysis of Data. 6. Partial Differential Equations I: Foundations and Explicit Methods. 7. Partial Differential Equations II: Advanced Explicit Methods. 8. Partial Differential Equations III: Relaxation and Spectral Methods. 9. Partial Differential Equations IV: Stability and Implicit Methods. 10. Special Functions and Quadrature. 11. Stochastic Methods.

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What this paper is about

1. Preliminaries. 2. Ordinary Differential Equations I: Basic Methods. 3. Ordinary Differential Equations II: Advanced Methods. 4. Solving Systems of Equations. 5. Analysis of Data. 6. Partial Differential Equations I: Foundations and Explicit Methods. 7. Partial Differential Equations II: Advanced Explicit Methods. 8. Partial Differential Equations III: Relaxation and Spectral Methods. 9. Partial Differential Equations IV: Stability and Implicit Methods. 10. Special Functions and Quadrature. 11. Stochastic Methods.

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Available abstract

1. Preliminaries. 2. Ordinary Differential Equations I: Basic Methods. 3. Ordinary Differential Equations II: Advanced Methods. 4. Solving Systems of Equations. 5. Analysis of Data. 6. Partial Differential Equations I: Foundations and Explicit Methods. 7. Partial Differential Equations II: Advanced Explicit Methods. 8. Partial Differential Equations III: Relaxation and Spectral Methods. 9. Partial Differential Equations IV: Stability and Implicit Methods. 10. Special Functions and Quadrature. 11. Stochastic Methods.

Key concepts: Numerical partial differential equations, Exponential integrator, Stochastic partial differential equation, Separable partial differential equation, Mathematics, Collocation method, Multigrid method, Method of characteristics

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