An efficient spectral approximation for solving several types of parabolic PDEs with nonlocal boundary conditions

DOI10.1155/2014/369029zbMath1407.65228OpenAlexW2043316676WikidataQ59064693 ScholiaQ59064693MaRDI QIDQ1718206

Adem Kilicman, Emran Tohidi

Publication date: 8 February 2019

Published in: Mathematical Problems in Engineering (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1155/2014/369029

Mathematics Subject Classification ID

Heat equation (35K05) Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs (65M70)

Related Items (8)

Generalized Laplace-type transform method for solving multilayer diffusion problems ⋮ On two‐dimensional weakly singular fractional partial integro‐differential equations and dual Bernstein polynomials ⋮ A new wavelet method for solving a class of nonlinear partial integro-differential equations with weakly singular kernels ⋮ An accurate space-time pseudospectral method for solving nonlinear multi-dimensional heat transfer problems ⋮ Bernoulli collocation method for solving linear multidimensional diffusion and wave equations with Dirichlet boundary conditions ⋮ Solving parabolic integro-differential equations with purely nonlocal conditions by using the operational matrices of Bernstein polynomials ⋮ A novel study based on Lerch polynomials for approximate solutions of pure Neumann problem ⋮ The solution of the nonlinear mixed partial integro-differential equation via two-dimensional hybrid functions

Cites Work

• A collocation method based on the Bernoulli operational matrix for solving high-order linear complex differential equations in a rectangular domain
• A collocation method based on the Bernoulli operational matrix for solving nonlinear BVPs which arise from the problems in calculus of variation
• The operational matrices of Bernstein polynomials for solving the parabolic equation subject to specification of the mass
• Galerkin method applied to a parabolic evolution problem with nonlocal boundary conditions
• A Legendre-Gauss collocation method for neutral functional-differential equations with proportional delays
• Solving a parabolic PDE with nonlocal boundary conditions using the sinc method
• A numerical solution for non-classical parabolic problem based on Chebyshev spectral collocation method
• Numerical solution of a nonclassical parabolic problem: an integro-differential approach
• A tau method approach for the diffusion equation with nonlocal boundary conditions

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