Journal ArticleDOI
Orthogonal spline collocation methods for some partial integrodifferential equations
Yi Yan,Graeme Fairweather +1 more
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In this article, the Laplace transform is introduced to analyze the method of orthogonal spline collocation for semidiscretization of a class of linear partial integrodifferential equations arising in viscoelasticity problems.Abstract:
The Laplace transform is introduced to analyze the method of orthogonal spline collocation for the semidiscretization of a class of linear partial integrodifferential equations arising in viscoelasticity problems, for example. The stability and convergence of the space discretization are examined.read more
Citations
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Journal ArticleDOI
A finite difference scheme for partial integro-differential equations with a weakly singular kernel
TL;DR: In this paper, a finite difference method for the numerical solution of partial integro-differential equations is considered and the convergence order in time is shown to be greater than one, which is confirmed by a numerical example.
Journal ArticleDOI
A second-order accurate numerical method for a fractional wave equation
William McLean,Kassem Mustapha +1 more
TL;DR: A generalized Crank–Nicolson scheme for the time discretization of a fractional wave equation, in combination with a space discretized by linear finite elements is studied.
Journal ArticleDOI
Numerical solution of an evolution equation with a positive-type memory term
William McLean,Vidar Thomée +1 more
TL;DR: In this paper, the numerical solution of an initial-boundary value problem for a Volterra type integro-differential equation, in which the integral operator is a convolution product of a positive-definite kernel and an elliptic partial differential operator, is studied.
Journal ArticleDOI
Orthogonal spline collocation methods for partial differential equations
TL;DR: An overview of orthogonal spline collocation (OSC) methods for the numerical solution of partial differential equations in two space variables is given in this article, with emphasis on alternating direction implicit methods.
Journal ArticleDOI
Solution of a partial integro-differential equation arising from viscoelasticity
TL;DR: Several computational techniques based on finite-difference schemes and the product trapezoidal numerical integration rule are constructed for determining the solution of a partial integro-differential equation subject to an initial condition and given boundary conditions.
References
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Book
Spline Functions: Basic Theory
TL;DR: The material covered provides the reader with the necessary tools for understanding the many applications of splines in such diverse areas as approximation theory, computer-aided geometric design, curve and surface design and fitting, image processing, numerical solution of differential equations, and increasingly in business and the biosciences.
Journal ArticleDOI
A general theory of heat conduction with finite wave speeds
TL;DR: In this article, the authors developed a general theory of heat conduction for nonlinear materials with memory, a theory which has associated with it finite propagation speeds, i.e., a thermal disturbance at any point in the body is felt instantly at every other point; or in terms more suggestive than precise, the speed of propagation of disturbances is infinite.
Book
Mathematical analysis of viscoelastic flows
TL;DR: In this paper, the authors present a survey of non-Newtonian flows with a focus on simple flows, including Reentrant Corner Singularities and change of type.
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Numerical solution of an evolution equation with a positive-type memory term
William McLean,Vidar Thomée +1 more