A new matrix approach for solving second-order linear matrix partial differential equations

DOI10.1007/s00009-015-0542-2zbMath1350.35061OpenAlexW2048019147MaRDI QIDQ327382

Mohammad Khorsand Zak, Emran Tohidi

Publication date: 19 October 2016

Published in: Mediterranean Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00009-015-0542-2

zbMATH Keywords

Bernoulli polynomialsoperational matricesgeneralized Sylvester equationssubspace Krylov iterative methods

Mathematics Subject Classification ID

Stability and convergence of numerical methods for ordinary differential equations (65L20) Theoretical approximation in context of PDEs (35A35) Numerical differentiation (65D25) Numerical integration (65D30) Integro-partial differential equations (35R09) Initial value problems for PDEs and systems of PDEs with constant coefficients (35E15)

Related Items

Eigenvalues and eigenfunctions of fourth-order Sturm-Liouville problems using Bernoulli series with Chebychev collocation points ⋮ Approximation properties of \(q\)-Bernoulli polynomials ⋮ Refinement of multiparameters overrelaxation (RMPOR) method ⋮ Robust bivariate polynomials scheme with convergence analysis for two-dimensional nonlinear optimal control problem ⋮ Two-dimensional shifted Legendre polynomials operational matrix method for solving the two-dimensional integral equations of fractional order ⋮ Application of Bernoulli matrix method for solving two-dimensional hyperbolic telegraph equations with Dirichlet boundary conditions ⋮ A new matrix method for solving two-dimensional time-dependent diffusion equations with Dirichlet boundary conditions ⋮ Two-dimensional Euler polynomials solutions of two-dimensional Volterra integral equations of fractional order ⋮ Lagrange operational matrix methods to Lane-Emden, Riccati's and Bessel's equations ⋮ An operational matrix based scheme for numerical solutions of nonlinear weakly singular partial integro-differential equations ⋮ Latest inversion-free iterative scheme for solving a pair of nonlinear matrix equations ⋮ On Bernoulli matrix polynomials and matrix exponential approximation ⋮ Two‐dimensional shifted Legendre polynomial collocation method for electromagnetic waves in dielectric media via almost operational matrices

Cites Work

• Unnamed Item
• A new approach for solving a system of fractional partial differential equations
• Fourier operational matrices of differentiation and transmission: introduction and applications
• Robustness of operational matrices of differentiation for solving state-space analysis and optimal control problems
• A collocation method based on the Bernoulli operational matrix for solving high-order linear complex differential equations in a rectangular domain
• Solving initial-boundary value problems for systems of partial differential equations using neural networks and optimization techniques
• Numerical simulations of systems of PDEs by variational iteration method
• The operational matrices of Bernstein polynomials for solving the parabolic equation subject to specification of the mass
• A new Bernoulli matrix method for solving second order linear partial differential equations with the convergence analysis
• An implicit difference method for the numerical solution of coupled systems of partial differential equations
• Symbolic semi-discretization of partial differential equation systems.
• An efficient numerical approach for solving nonlinear coupled hyperbolic partial differential equations with nonlocal conditions
• A block version of BiCGSTAB for linear systems with multiple right-hand sides
• Global FOM and GMRES algorithms for matrix equations
• Taylor polynomial solutions of second order linear partial differential equations
• A note on the numerical approximate solutions for generalized Sylvester matrix equations with applications
• Chebyshev polynomial approximation for high‐order partial differential equations with complicated conditions
• Bi-CGSTAB: A Fast and Smoothly Converging Variant of Bi-CG for the Solution of Nonsymmetric Linear Systems
• Wendroff Type Inequalities
• Double Walsh series solution of first-order partial differential equations
• Computing accurate solutions for coupled systems of second order partial differential equations II
• Expansion over a rectangle of real functions in Bernoulli polynomials and applications

This page was built for publication: A new matrix approach for solving second-order linear matrix partial differential equations