Orthogonal rational functions on a semi-infinite interval
Journal of Computational Physics
Spectral methods using rational basis functions on an infinite interval
Journal of Computational Physics
Collocation methods for second-order Volterra integro-differential equations
Applied Numerical Mathematics
Solving parabolic integro-differential equations by an explicit integration method
Journal of Computational and Applied Mathematics
A finite difference scheme for partial integro-differential equations with a weakly singular kernel
Applied Numerical Mathematics
Chebyshev spectral solution of nonlinear Volterra-Hammerstein integral equations
Journal of Computational and Applied Mathematics
Error estimation of Hermite spectral method for nonlinear partial differential equations
Mathematics of Computation
On the computation of high order pseudospectral derivatives
Proceedings of the fourth international conference on Spectral and high order methods (ICOSAHOM 1998)
A Rational Approximation and Its Applications to Differential Equations on the Half Line
Journal of Scientific Computing
Stable and Efficient Spectral Methods in Unbounded Domains Using Laguerre Functions
SIAM Journal on Numerical Analysis
Mathematics and Computers in Simulation
A pseudospectral method of solution of Fisher's equation
Journal of Computational and Applied Mathematics
Analysis of a Spectral-Galerkin Approximation to the Helmholtz Equation in Exterior Domains
SIAM Journal on Numerical Analysis
Journal of Computational Physics
Chebyshev finite difference method for Fredholm integro-differential equation
International Journal of Computer Mathematics
Pseudospectral method of solution of the Fitzhugh-Nagumo equation
Mathematics and Computers in Simulation
On spectral methods for Volterra-type integro-differential equations
Journal of Computational and Applied Mathematics
Applied Numerical Mathematics
A meshless based method for solution of integral equations
Applied Numerical Mathematics
Computers & Mathematics with Applications
Numerical solution of fourth-order integro-differential equations using Chebyshev cardinal functions
International Journal of Computer Mathematics
Applied Numerical Mathematics
The Sinc-collocation method for solving the Thomas-Fermi equation
Journal of Computational and Applied Mathematics
Applied Numerical Mathematics
Journal of Computational and Applied Mathematics
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In this paper we study the numerical solutions to parabolic Volterra integro-differential equations in one-dimensional bounded and unbounded spatial domains. In a bounded domain, the given parabolic Volterra integro-differential equation is converted to two equivalent equations. Then, a Legendre-collocation method is used to solve them and finally a linear algebraic system is obtained. For an unbounded case, we use the algebraic mapping to transfer the problem on a bounded domain and then apply the same presented approach for the bounded domain. In both cases, some numerical examples are presented to illustrate the efficiency and accuracy of the proposed method.