Browsing by Subject "Partial differential equations"
Now showing items 41-48 of 48
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Article
A survey of applications of the MFS to inverse problems
(2011)The method of fundamental solutions (MFS) is a relatively new method for the numerical solution of boundary value problems and initial/boundary value problems governed by certain partial differential equations. The ease ...
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Article
Symmetries and form-preserving transformations of generalised inhomogeneous nonlinear diffusion equations
(2003)We consider the variable coefficient inhomogeneous nonlinear diffusion equations of the form f(x)ut = [g(x)unux]x. We present a complete classification of Lie symmetries and form-preserving point transformations in the ...
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Article
Symmetries and form-preserving transformations of one-dimensional wave equations with dissipation
(2001)General results are given for the forms of infinitesimal point symmetries of the class of partial differential equations in which utt is a function of x,t,u,ut and the x-derivatives of u up to order n ≥ 2. Continuous and ...
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Article
Symmetry analysis of a model for the exercise of a barrier option
(2013)A barrier option takes into account the possibility of an unacceptable change in the price of the underlying stock. Such a change could carry considerable financial loss. We examine one model based upon the Black-Scholes-Merton ...
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Article
Symmetry analysis of a model of stochastic volatility with time-dependent parameters
(2011)We provide the solutions for the Heston model of stochastic volatility when the parameters of the model are constant and when they are functions of time. In the former case, the solution follows immediately from the ...
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Symmetry and singularity analyses of some equations of the fifth and sixth order in the spatial variable arising from the modelling of thin films
(2013)In the modelling of the flow of thin films higher-order derivatives in the spatial variable are introduced to model nonlinear effects. We examine nonlinear evolution equations of the fifth and sixth orders in the spatial ...
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Article
Thin films: Increasing the complexity of the model
(2012)Thin films arise in a variety of contexts. They can be between two solid surfaces in the form of a lubricant or with one surface solid and the other free as in water or oil on a road. When the surface tension is a dominant ...
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Article
Transformation properties of a variable-coefficient Burgers equation
(2004)In this paper we consider the variable coefficient equation u t=b(t)uux+a(t)uxx which among other applications has considerable interest in nonlinear acoustics. We present transformation properties of this generalised ...