Numerical solutions of linear and nonlinear diffusion equations by a differential quadrature method (DQM)

DOI10.1002/cnm.1292zbMath1210.65175OpenAlexW2030781484MaRDI QIDQ3084137

Gurhan Gurarslan, Murat Sari

Publication date: 15 March 2011

Published in: International Journal for Numerical Methods in Biomedical Engineering (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1002/cnm.1292

zbMATH Keywords

numerical examplesRunge-Kutta methoddifferential quadrature methodstrong stability preservinglinear and nonlinear diffusion equations

Mathematics Subject Classification ID

Nonlinear parabolic equations (35K55) Heat equation (35K05) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs (65M70)

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Cites Work

• Unnamed Item
• The variational iteration method: a powerful scheme for handling linear and nonlinear diffusion equations
• Numerical solutions of the generalized Burgers-Huxley equation by a differential quadrature method
• Integral results for nonlinear diffusion equations
• The non-classical solution for the inhomogeneous nonlinear diffusion equation
• A localized differential quadrature (LDQ) method and its application to the 2D wave equation
• Several new exact solutions for a fast diffusion equation by the differential constraints of the linear determining equations
• Exact solutions to nonlinear diffusion equations obtained by the decomposition method
• Approximations of Sturm-Liouville eigenvalues using differential quadrature (DQ) method
• Differential quadrature: A technique for the rapid solution of nonlinear partial differential equations
• Nonlinear partial differential equations in engineering. Vol. II
• Strong Stability-Preserving High-Order Time Discretization Methods
• Differential quadrature method (DQM) for a class of singular two-point boundary value problems
• Application of generalized differential quadrature to solve two-dimensional incompressible Navier-Stokes equations
• Linear determining equations for differential constraints
• Exact solutions to nonlinear diffusion equations obtained by a generalized conditional symmetry method
• New classes of similarity solutions of the inhomogeneous nonlinear diffusion equations
• Determining equations in diffusion problems