The numerical solution of semidiscrete linear evolution problems on the finite interval using the Unified Transform Method
DOI10.1090/QAM/1626zbMath1496.65145arXiv2112.01631OpenAlexW4293743824MaRDI QIDQ5099123
Jorge Cisneros, Bernard Deconinck
Publication date: 31 August 2022
Published in: Quarterly of Applied Mathematics (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2112.01631
continuum limitfinite differencefinite intervalghost pointsunified transform methodsemidiscrete linear problem
Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Partial difference equations (39A14) Numerical solution of discretized equations for initial value and initial-boundary value problems involving PDEs (65M22) Fictitious domain methods for boundary value problems involving PDEs (65N85) Boundary value problems for difference equations (39A27)
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Finite-difference ghost-point multigrid methods on Cartesian grids for elliptic problems in arbitrary domains
- Adaptive mesh refinement based on high order finite difference WENO scheme for multi-scale simulations
- Novel numerical techniques based on Fokas transforms, for the solution of initial boundary value problems
- The modified equation approach to the stability and accuracy analysis of finite-difference methods
- Stable second-order finite-difference methods for linear initial-boundary-value problems
- Finite Difference Computing with PDEs
- Initial-boundary-value problems for discrete linear evolution equations
- A Unified Approach to Boundary Value Problems
- A First Course in the Numerical Analysis of Differential Equations
- Initial-boundary-value problems for discrete evolution equations: discrete linear Schrödinger and integrable discrete nonlinear Schrödinger equations
- Numerical Methods for Fluid Dynamics
- Numerical Methods Based on Additive Splittings for Hyperbolic Partial Differential Equations
- Intermediate Boundary Conditions for Time-Split Methods Applied to Hyperbolic Partial Differential Equations
- Stability Theory of Difference Approximations for Mixed Initial Boundary Value Problems. II
- A unified transform method for solving linear and certain nonlinear PDEs
- A numerical implementation of the unified Fokas transform for evolution problems on a finite interval
- The numerical solutions of linear semidiscrete evolution problems on the half‐line using the Unified Transform Method
- The numerical unified transform method for initial-boundary value problems on the half-line
- Kernel density estimation with linked boundary conditions
- Discrete linear evolution equations in a finite lattice
- Unified Transform for Boundary Value Problems
- An explicit harmonic code for black-hole evolution using excision
- A hybrid analytical–numerical method for solving evolution partial differential equations. I. The half-line
- Operator Splitting
- The Method of Fokas for Solving Linear Partial Differential Equations
This page was built for publication: The numerical solution of semidiscrete linear evolution problems on the finite interval using the Unified Transform Method