An operational matrix based scheme for numerical solutions of nonlinear weakly singular partial integro-differential equations

DOI10.1016/j.amc.2019.124771zbMath1433.65365OpenAlexW2978113998WikidataQ127185059 ScholiaQ127185059MaRDI QIDQ2284797

Yanyan Li

Publication date: 15 January 2020

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

Full work available at URL: https://doi.org/10.1016/j.amc.2019.124771

zbMATH Keywords

Legendre waveletsoperational matrixBernoulli waveletsweakly singular partial integro-differential equation

Mathematics Subject Classification ID

Bernoulli and Euler numbers and polynomials (11B68) Integro-ordinary differential equations (45J05) Numerical methods for integral equations (65R20) Numerical methods for wavelets (65T60) Volterra integral equations (45D05) Integro-partial differential equations (35R09)

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Cites Work

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• A new matrix approach for solving second-order linear matrix partial differential equations
• Modified Euler's method with a graded mesh for a class of Volterra integral equations with weakly singular kernel
• Comparative experiment on the numerical solutions of Hammerstein integral equation arising from chemical phenomenon
• Two-dimensional wavelets collocation method for electromagnetic waves in dielectric media
• A nonlinear weakly singular Volterra integro-differential equation arising from a reaction-diffusion study in a small cell
• Wavelet Galerkin method for solving singular integral equations
• Legendre spectral collocation method for the solution of the model describing biological species living together
• A new Bernoulli matrix method for solving second order linear partial differential equations with the convergence analysis
• High accuracy combination method for solving the systems of nonlinear Volterra integral and integro-differential equations with weakly singular kernels of the second kind
• Approximate controllability of semilinear system with state delay using sequence method
• Computational implementation of the inverse continuous wavelet transform without a requirement of the admissibility condition
• A new matrix method for solving two-dimensional time-dependent diffusion equations with Dirichlet boundary conditions
• Two dimensional wavelets collocation scheme for linear and nonlinear Volterra weakly singular partial integro-differential equations
• Superconvergence of numerical solutions to weakly singular Volterra integro-differential equations
• Convergence analysis of Bernoulli matrix approach for one-dimensional matrix hyperbolic equations of the first order
• A new Bernoulli wavelet method for accurate solutions of nonlinear fuzzy Hammerstein-Volterra delay integral equations
• A new Bernoulli matrix method for solving high-order linear and nonlinear Fredholm integro-differential equations with piecewise intervals
• A general theory of heat conduction with finite wave speeds
• An integro-differential equation with application in heat flow
• Convergence rate of collocation method based on wavelet for nonlinear weakly singular partial integro‐differential equation arising from viscoelasticity
• A numerical approach for solving weakly singular partial integro‐differential equations via two‐dimensional‐orthonormal Bernstein polynomials with the convergence analysis

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