[[CSDMS meeting abstract presentation::I will give a overview of the basic foundations of numerical methods for modeling earth systems described by ordinary and partial differential equations. I will discuss the underlying foundations of finite-difference, finite-volume and finite-element methods using diffusion/conduction equations as an example. I will discuss explicit and implicit methods for time-stepping, and stability analysis of time-integration schemes. All numerical methods for ODEs and PDEs in some form arrive at algebraic approximations, translating them into systems of algebraic equations. I will discuss basic algorithms for solving systems of algebraic equations, and how they are incorporated into various software packages, and also emphasize the importance of sparsity in matrix computations. I will include examples derived from practical problems in reactive transport and glacier dynamics to illustrate how basic concepts apply to real-world problems and make a difference when we want to develop efficient and accurate models.
PDFs of the numerical methods for scientific computing clinic
Numerical methods for scientific computing clinic example files:
1) Newton Raphson Iteration for solving nonlinear equations pdf
2) Solution of Laplace pdf
3) Illustration using the 1D heat equation pdf
* Matlab files: zip