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Article
Singularity separation Chebyshev collocation method for weakly singular Volterra integral equations of the second kind
Volterra integral equation of the second kind with weakly singular kernel usually exhibits singular behavior at the origin, which deteriorates the accuracy of standard numerical methods. This paper develops a ...
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Article
The series expansions and blow-up time estimation for the solutions of convolution Volterra-Hammerstein integral equations
The blow-up phenomenon may occur in nonlinear integral equations and differential equations, which has important significance for the simulation of some practical problems. This paper is devoted to predicting ...
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Article
The High Order Augmented Finite Volume Methods Based on Series Expansion for Nonlinear Degenerate Parabolic Equations
Two high order multi-augmented and improved augmented finite volume methods are proposed for solving nonlinear degenerate parabolic problems. The solution is represented as Puiseux series expansion in a subdom...
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Article
The series expansion and Chebyshev collocation method for nonlinear singular two-point boundary value problems
The solution of singular two-point boundary value problem is usually not sufficiently smooth at one or two endpoints of the interval, which leads to a great difficulty when the problem is solved numerically. I...
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Article
The asymptotic approximations to linear weakly singular Volterra integral equations via Laplace transform
In this paper, the asymptotic expansions for the solution about zero and infinity are formulated via Laplace transform for linear Volterra integral equation with weakly singular convolution kernel. The expansi...
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Article
The Puiseux Expansion and Numerical Integration to Nonlinear Weakly Singular Volterra Integral Equations of the Second Kind
This paper develops an efficient algorithm to solve nonlinear Volterra integral equation of the second kind with weakly singular convolution kernel. First, we show that the general Puiseux series for the solut...
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Article
An algorithm for the inversion of Laplace transforms using Puiseux expansions
This paper is devoted to designing a practical algorithm to invert the Laplace transform by assuming that the transform possesses the Puiseux expansion at infinity. First, the general asymptotic expansion of t...
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Article
The practical Gauss type rules for Hadamard finite-part integrals using Puiseux expansions
A general framework is constructed for efficiently and stably evaluating the Hadamard finite-part integrals by composite quadrature rules. Firstly, the integrands are assumed to have the Puiseux expansions at ...
