Numerical Solution of the Neural Field Equation in the Two-Dimensional Case

DOI10.1137/15M1022562zbMath1329.65316arXiv1508.07484OpenAlexW2963234875MaRDI QIDQ3457825

Evelyn Buckwar, Pedro M. Lima

Publication date: 18 December 2015

Published in: SIAM Journal on Scientific Computing (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1508.07484

zbMATH Keywords

complexityalgorithmconvergencenumerical exampleintegro-differential equationsChebyshev interpolationfixed point methodGaussian quadraturesneural field equations

Mathematics Subject Classification ID

Numerical methods for integral equations (65R20) Integro-partial differential equations (45K05) Neural biology (92C20) Complexity and performance of numerical algorithms (65Y20)

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Cites Work

• A fast iterative method for discretized Volterra-Fredholm integral equations
• Some theoretical and numerical results for delayed neural field equations
• A fast numerical solution method for two dimensional Fredholm integral equations of the second kind
• Continuous time collocation methods for Volterra-Fredholm integral equations
• Dynamics of pattern formation in lateral-inhibition type neural fields
• Asymptotic error expansion for the Nyström method for a nonlinear Volterra-Fredholm integral equation
• Numerical solution of a Fredholm integro-differential equation modelling \(\dot \theta\)-neural networks
• Numerical solution of a Fredholm integro-differential equation modelling neural networks
• On the Numerical Solution of Nonlinear Volterra–Fredholm Integral Equations by Collocation Methods
• Existence and properties of solutions for neural field equations
• Numerical Simulation Scheme of One- and Two Dimensional Neural Fields Involving Space-Dependent Delays

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