Tag
implicit-methods
- May 20, 2026 A-Stability and the Dahlquist Barrier Why the second Dahlquist barrier limits linear multistep methods to order two when they must damp every decaying mode, and how the equivalent restrictions apply to Runge-Kutta schemes. scientific computing
- 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 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
- Apr 6, 2023 Stiffness: When Explicit Steps Collapse What makes an initial value problem stiff, why an explicit method is forced to steps far below what accuracy requires, and how the Jacobian eigenvalues set the forced step. scientific computing