Superconvergence results of Legendre spectral projection methods for Volterra integral equations of second kind
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DOI: 10.1007/s40314-017-0563-5
Abstract: In this paper, Legendre spectral projection methods are applied for the Volterra integral equations of second kind with a smooth kernel. We prove that the approximate solutions of the Legendre Galerkin and Legendre collocation methods… read more here.
Keywords: order; spectral projection; order mathcal; legendre spectral ... See more keywords
Legendre Spectral Projection Methods for Hammerstein Integral Equations with Weakly Singular Kernel
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DOI: 10.1007/s40819-018-0580-0
Abstract: In this paper, we consider the Legendre Galerkin and Legendre collocation methods for solving the Fredholm–Hammerstein integral equation with weakly singular kernels. We evaluate the convergence rates for both the methods in both $$L^2$$L2 and… read more here.
Keywords: spectral projection; legendre galerkin; legendre spectral; iterated legendre ... See more keywords
Applications of Legendre spectral collocation method for solving system of time delay differential equations
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DOI: 10.1177/1687814020922113
Abstract: The numerical techniques are regarded as the backbone of modern research. In literature, the exact solution of time delay differential models are hardly achievable or impossible. Therefore, numerical techniques are the only way to find… read more here.
Keywords: system; legendre spectral; method; time delay ... See more keywords
Legendre spectral element method for solving sine-Gordon equation
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DOI: 10.1186/s13662-019-2059-7
Abstract: In this paper, we study the Legendre spectral element method for solving the sine-Gordon equation in one dimension. Firstly, we discretize the equation by Legendre spectral element in space and then discretize the time by… read more here.
Keywords: legendre spectral; spectral element; method; equation ... See more keywords