Improvement of He's variational iteration method for solving systems of differential equations
Computers & Mathematics with Applications
He's variational iteration method for solving nonlinear mixed Volterra-Fredholm integral equations
Computers & Mathematics with Applications
Computers & Mathematics with Applications
Journal of Computational and Applied Mathematics
The spectral methods for parabolic Volterra integro-differential equations
Journal of Computational and Applied Mathematics
SIAM Journal on Scientific Computing
An approximation method for solving systems of Volterra integro-differential equations
Applied Numerical Mathematics
Journal of Computational and Applied Mathematics
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Particular cases of nonlinear systems of delay Volterra integro-differential equations (denoted by DVIDEs) with constant delay τ 0, arise in mathematical modelling of ‘predator–prey’ dynamics in Ecology. In this paper, we give an analysis of the global convergence and local superconvergence properties of piecewise polynomial collocation for systems of this type. Then, from the perspective of applied mathematics, we consider the Volterra’s integro-differential system of ‘predator–prey’ dynamics arising in Ecology. We analyze the numerical issues of the introduced collocation method applied to the ‘predator–prey’ system and confirm that we can achieve the expected theoretical orders of convergence.