Tag
finite-difference
- Apr 30, 2025 Newton Iterations for Implicit Spatial Operators How an implicit step on a nonlinear PDE becomes a Newton solve on a sparse system, what convergence the iteration has, and why the Jacobian is assembled from the stencil. scientific computing
- Feb 19, 2025 Global Error Accumulation and the CFL Condition How local truncation errors combine across steps, why the von Neumann analysis of explicit advection produces the Courant number bound, and what propagation velocity has to do with it. scientific computing
- Feb 25, 2024 The Parabolic Step Limit in Explicit Diffusion Schemes Why an explicit update of the heat equation requires a step proportional to the square of the mesh spacing, what the amplification analysis shows, and how implicit treatment removes the restriction. scientific computing