Boundary integral formulation and semi-implicit scheme coupling for modeling cells under electrical stimulation

DOI10.1007/s00211-016-0835-9zbMath1362.65098OpenAlexW2478404927MaRDI QIDQ527819

Fernando Henríquez, Fernando Altermatt, Carlos Jerez-Hanckes

Publication date: 12 May 2017

Published in: Numerische Mathematik (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00211-016-0835-9

zbMATH Keywords

stabilityconvergenceGalerkin methodexistenceuniquenessnumerical experimentsLaplace equationboundary integral formulationHodgkin-Huxley modelbiological cellelectrical stimulationsecond-order time-steppingunsteady transmission problem

Mathematics Subject Classification ID

Numerical methods for integral equations (65R20) Neural biology (92C20) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Boundary element methods for initial value and initial-boundary value problems involving PDEs (65M38)

Related Items

Local multiple traces formulation for electromagnetics: stability and preconditioning for smooth geometries, Derivation of cable equation by multiscale analysis for a model of myelinated axons, Multiple traces formulation and semi-implicit scheme for modelling biological cells under electrical stimulation, An Overview on Steffensen-Type Methods, Multiscale Analysis of Myelinated Axons

Uses Software

• PETSc

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• High-order accurate difference schemes for the Hodgkin-Huxley equations
• Multiple traces boundary integral formulation for Helmholtz transmission problems
• Galerkin finite element methods for parabolic problems
• A fully discrete \(H^1\)-Galerkin method with quadrature for nonlinear advection-diffusion-reaction equations
• Boundary integral equations
• Global existence and uniqueness of a three-dimensional model of cellular electrophysiology
• Mathematical physiology. I: Cellular physiology
• Existence and uniqueness for an elliptic problem with evolution arising in electrodynamics
• A maximum principle for an explicit finite difference scheme approximating the Hodgkin-Huxley model
• Numerical Approximation Methods for Elliptic Boundary Value Problems
• Reaction–diffusion systems for the microscopic cellular model of the cardiac electric field
• Semi-Implicit Time-Discretization Schemes for the Bidomain Model
• Boundary Integral Operators on Lipschitz Domains: Elementary Results
• Implicit-explicit multistep finite element methods for nonlinear parabolic problems
• Implicit-Explicit Methods for Time-Dependent Partial Differential Equations
• Relations Between Redundancy Patterns of the Shannon Code and Wave Diffraction Patterns of Partially Disordered Media
• Multitrace boundary integral equations
• Boundary Element Methods