A collocation method using Hermite polynomials for approximate solution of pantograph equations

DOI10.1016/j.jfranklin.2011.05.003zbMath1221.65187OpenAlexW2002458302MaRDI QIDQ553566

Mehmet Sezer, Müge Aynigül, Salih Fuat Yalçinbaş

Publication date: 27 July 2011

Published in: Journal of the Franklin Institute (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jfranklin.2011.05.003

zbMATH Keywords

collocation methodnumerical examplesHermite polynomialgeneralized pantograph equations

Mathematics Subject Classification ID

Related Items (46)

Solving generalized pantograph equations by shifted orthonormal Bernstein polynomials ⋮ Numerical analysis of pantograph differential equation of the stretched type associated with fractal-fractional derivatives via fractional order Legendre wavelets ⋮ A compatible Hermite-Taylor matrix-collocation technique with convergence test for second-order partial integro-differential equations containing two independent variables with functional bounds ⋮ An alternative use of fuzzy transform with application to a class of delay differential equations ⋮ Stochastic approach for the solution of multi-pantograph differential equation arising in cell-growth model ⋮ Numerical solution of pantograph-type delay differential equations using perturbation-iteration algorithms ⋮ A highly accurate Jacobi collocation algorithm for systems of high‐order linear differential–difference equations with mixed initial conditions ⋮ A collocation method based on Bernoulli operational matrix for numerical solution of generalized pantograph equation ⋮ A new numerical method to solve pantograph delay differential equations with convergence analysis ⋮ Unnamed Item ⋮ Lucas polynomial approach for system of high-order linear differential equations and residual error estimation ⋮ 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 ⋮ Modified Chebyshev collocation method for pantograph-type differential equations ⋮ Solution of Benjamin-Bona-Mahony-Burgers equation using collocation method with quintic Hermite splines ⋮ Generalized Lucas polynomial sequence treatment of fractional pantograph differential equation ⋮ A new Fibonacci type collocation procedure for boundary value problems ⋮ A novel mesh discretization strategy for numerical solution of optimal control problems in aerospace engineering ⋮ Approximate solution of nonlinear optimal control problems with scale delay function via a composite pseudospectral approach ⋮ Numerical solutions of optimal control for linear Volterra integrodifferential systems via hybrid functions ⋮ Generalized difference simulation for coupled transport models of unsaturated soil water flow and solute ⋮ Unnamed Item ⋮ A new Bernoulli matrix method for solving high-order linear and nonlinear Fredholm integro-differential equations with piecewise intervals ⋮ Numerical solution of nonlinear fractional Volterra integro-differential equations via Bernoulli polynomials ⋮ A new Jacobi rational-Gauss collocation method for numerical solution of generalized pantograph equations ⋮ A collocation method based on the Bernoulli operational matrix for solving nonlinear BVPs which arise from the problems in calculus of variation ⋮ Numeric solutions for the pantograph type delay differential equation using first Boubaker polynomials ⋮ Collocation method based on radial basis functions via symmetric variable shape parameter for solving a particular class of delay differential equations ⋮ A Taylor operation method for solutions of generalized pantograph type delay differential equations ⋮ A new collocation method for approximate solution of the pantograph functional differential equations with proportional delay ⋮ A new spectral method for a class of linear boundary value problems ⋮ Laguerre matrix method with the residual error estimation for solutions of a class of delay differential equations ⋮ Orthogonal polynomials and Möbius transformations ⋮ Direct operatorial tau method for pantograph-type equations ⋮ A new computational approach for the solutions of generalized pantograph-delay differential equations ⋮ An exponential approximation for solutions of generalized pantograph-delay differential equations ⋮ Shifted Legendre approximation with the residual correction to solve pantograph-delay type differential equations ⋮ A numerical approach for solving Volterra type functional integral equations with variable bounds and mixed delays ⋮ A rational approximate solution for generalized pantograph-delay differential equations ⋮ Taylor matrix method for solving linear two-dimensional Fredholm integral equations with piecewise intervals ⋮ An exploration of quintic Hermite splines to solve Burgers' equation ⋮ Approximation methods for solving fractional optimal control problems ⋮ Numerical solution of multi-pantograph delay boundary value problems via an efficient approach with the convergence analysis ⋮ Rigorous convergence analysis of Jacobi spectral Galerkin methods for Volterra integral equations with noncompact kernels ⋮ A Bessel collocation method for solving fractional optimal control problems

Cites Work

• Unnamed Item
• Unnamed Item
• A new polynomial approach for solving difference and Fredholm integro-difference equations with mixed argument
• A Taylor method for numerical solution of generalized pantograph equations with linear functional argument
• The pantograph equation in the complex plane
• Properties of analytic solution and numerical solution of multi-pantograph equation
• Generalized refinement equations and subdivision processes
• Approximate solution of multi-pantograph equation with variable coefficients
• The approximate solution of high-order linear difference equations with variable coefficients in terms of Taylor polynomials
• A Taylor polynomial approach for solving differential-difference equations
• Laguerre series solution of a functional differential equation
• Walsh stretch matrices and functional differential equations
• Analysis of a Model Representing Stage-Structured Population Growth with State-Dependent Time Delay
• A method for the approximate solution of the second‐order linear differential equations in terms of Taylor polynomials
• The Adomian decomposition method for solving delay differential equation
• On the asymptotics of solutions of a class of linear functional-differential equations
• A Taylor expansion approach for solving integral equations
• Stability of the Discretized Pantograph Differential Equation
• On a Functional Differential Equation
• The approximate solution of high-order linear Volterra-Fredholm integro-differential equations in terms of Taylor polynomials

This page was built for publication: A collocation method using Hermite polynomials for approximate solution of pantograph equations