A locally adaptive time stepping algorithm for the solution to reaction diffusion equations on branched structures

DOI10.1007/s10444-015-9437-9zbMath1341.65032OpenAlexW2298841787MaRDI QIDQ295380

Richard A. Kublik, David L. Chopp

Publication date: 13 June 2016

Published in: Advances in Computational Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10444-015-9437-9

zbMATH Keywords

algorithmconvergencenumerical examplesdomain decompositionreaction-diffusion equationsneural systemadaptive time-steppingHodgkin-Huxley equation

Mathematics Subject Classification ID

Reaction-diffusion equations (35K57) Neural networks for/in biological studies, artificial life and related topics (92B20) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Multigrid methods; domain decomposition for initial value and initial-boundary value problems involving PDEs (65M55)

Related Items (1)

Extended Synchronous Variational Integrators for Wave Propagations on Non-Uniform Meshes

Uses Software

• VODE
• NEURON
• DIFSUB
• CVODE

Cites Work

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• A bridging domain method for coupling continua with molecular dynamics
• Parallel network simulations with NEURON
• Mixed methods for time integration
• An implicit multi-time step integration method for structural dynamics problems
• Moving mesh methods with locally varying time steps
• A Finite Difference Domain Decomposition Algorithm for Numerical Solution of the Heat Equation
• The Backward Euler Method for Numerical Solution of the Hodgkin–Huxley Equations of Nerve Conduction
• VODE: A Variable-Coefficient ODE Solver
• A Polyalgorithm for the Numerical Solution of Ordinary Differential Equations
• Implicit-Explicit Parallel Asynchronous Solver of Parabolic PDEs
• Stabilized Explicit-Implicit Domain Decomposition Methods for the Numerical Solution of Parabolic Equations
• A Predictor‐Corrector Algorithm for Reaction‐Diffusion Equations Associated with Neural Activity on Branched Structures
• The automatic integration of ordinary differential equations
• Unconditional Stability of Corrected Explicit‐Implicit Domain Decomposition Algorithms for Parallel Approximation of Heat Equations

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