Fast Runge-Kutta approximation of inhomogeneous parabolic equations
María López-Fernández, Christian Lubich, Cesar Palencia, Achim Schädle
Abstract
The result after N steps of an implicit Runge-Kutta time discretization of an inhomogeneous linear parabolic differential equation is computed, up to accuracy ε, by solving only O( N 1ε) linear systems of equations. We derive, analyse, and numerically illustrate this fast algorithm.
Create a lesson
Related papers
Sensitivity Calculus and its Numerical Implementation for Multi-D Hyperbolic Balance Laws
Olivia Dreßen, Michael Herty, Adrian Kolb et al.
A Unified Framework for Wasserstein Convergence of ULMC Methods beyond Log-Concavity: Old and New
Wanjie Lyu, Xiaojie Wang, Bin Yang
Beyond PINNs: A Unified Gauss--Newton and Petrov--Galerkin Framework for Neural and Hybrid PDE Solvers
Nilo Schwencke, Roland Maier
Incremental Column Subset Selection via Conditional Determinantal Point Processes
Laura Grigori, Zhipeng Xue
A Hybrid High-Order Method for the Elasticity Problem with Linear Slip Interface
Erik Burman, Peiqi Huang
Adaptive Sparse-grid Discontinuous Galerkin Approximations the Bhatnagar--Gross--Krook Model
Stefan Schnake, Miroslav Stoyanov, Eirik Endeve et al.