Novel determination of differential-equation solutions: Universal approximation method

DOI10.1016/S0377-0427(02)00397-7zbMath1013.65079WikidataQ115339005 ScholiaQ115339005MaRDI QIDQ1860390

Thananchai Leephakpreeda

Publication date: 23 February 2003

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

zbMATH Keywords

finite elementLaplace equationfinite differenceneural network modelfuzzy linguistic modeluniversal approximation

Mathematics Subject Classification ID

Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Linear ordinary differential equations and systems (34A30) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Finite difference methods for boundary value problems involving PDEs (65N06) Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations (65L60) Numerical solution of boundary value problems involving ordinary differential equations (65L10) Finite difference and finite volume methods for ordinary differential equations (65L12)

Related Items (7)

Chebyshev neural network based model for solving Lane-Emden type equations ⋮ Solving initial-boundary value problems for systems of partial differential equations using neural networks and optimization techniques ⋮ Fuzzy linguistic model for interpolation ⋮ Universal approximation method for the solution of integral equations ⋮ Assessment of structural health monitoring by analyzing some modal parameters (I) (an inventory of methods and some developments) ⋮ Simulation and evaluation of second-order fuzzy boundary value problems ⋮ Solving Fokker-Planck equation using deep learning

Uses Software

• Optimization Toolbox

Cites Work

• General Takagi-Sugeno fuzzy systems with simplified linear rule consequent are universal controllers, models and filters
• Multilayer feedforward networks are universal approximators

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