Related papers: Numerical solutions of boundary value problems for…
There exist several approaches exploiting Lie symmetries in the reduction of boundary-value problems for partial differential equations modelling real-world phenomena to those problems for ordinary differential equations. Using an example…
Nonlinear boundary value problems (BVPs) by means of the classical Lie symmetry method are studied. A new definition of Lie invariance for BVPs is proposed by the generalization of existing those on much wider class of BVPs. A class of…
We introduce a method for efficiently solving initial-boundary value problems (IBVPs) that uses Lie symmetries to enforce the associated partial differential equation (PDE) exactly by construction. By leveraging symmetry transformations,…
This paper is concerned with a class of partial differential equations, which are the linear combinations, with constant coefficients, of the classical flows of the KdV hierarchy. A boundary value problem with inhomogeneous boundary…
An initial-boundary value problem for a generalized KdV equation posed on a half-line is considered. Existence and uniqueness of global regular solutions for arbitrary smooth initial data are established.
A new method is introduced for studying boundary value problems for a class of linear PDEs with {\it variable} coefficients. This method is based on ideas recently introduced by the author for the study of boundary value problems for PDEs…
To combine a feedforward neural network (FNN) and Lie group (symmetry) theory of differential equations (DEs), an alternative artificial NN approach is proposed to solve the initial value problems (IVPs) of ordinary DEs (ODEs). Introducing…
Lie symmetry method is applied to find analytic solutions of initial-boundary-value problems of transient conduction in semi-infinite solid with constant surface temperature or constant heat flux condition. The solutions are obtained in a…
Solutions of boundary value problems for a diffusion equation of fractional and variable order in differential and difference settings are studied. It is shown that the method of energy inequalities is applicable to obtaining a priori…
We investigated the analytical solution of fractional order K(m,n) type equation with variable coefficient which is an extended type of KdV equations into a genuinely nonlinear dispersion regime. By using the Lie symmetry analysis, we…
In this paper, nonlocal symmetries and exact solutions of variable coefficient Korteweg-de Vries (KdV) equation are studied for the first time. Using pseudo-potential, high order nonlocal symmetries of time-dependent coefficient KdV…
Solutions of the Dirichlet and Robin boundary value problems for the multi-term variable-distributed order diffusion equation are studied. A priori estimates for the corresponding differential and difference problems are obtained by using…
We study initial boundary value problems for linear scalar partial differential equations with constant coefficients, with spatial derivatives of {\em arbitrary order}, posed on the domain $\{t>0, 0<x<L\}$. We first show that by analysing…
In this article we study a class of generalised linear systems of difference equations with given boundary conditions and assume that the boundary value problem is non-consistent, i.e. it has infinite many or no solutions. We take into…
Group classification of classes of mKdV-like equations with time-dependent coefficients is carried out. The usage of equivalence transformations appears a crucial point for the exhaustive solution of the problem. We prove that all the…
In this work two-point boundary value problem for one class of second order ordinary differential equations with variable coefficients is solved.
This work investigates the application of the Newton's method for the numerical solution of a nonlinear boundary value problem formulated through an ordinary differential equation (ODE). Nonlinear ODEs arise in various mathematical modeling…
For a class of partial differential algebraic equations (PDAEs) of quasi-linear type which include nonlinear terms of convection type a possibility to determine a time and spatial index is considered. As a typical example we investigate an…
A definition of invariance in Lie's sense for a boundary value problem (BVP) with the basic evolution differential equations is proposed. A problem of group classification at a wide class of BVPs parameterized by arbitrary elements is…
A new definition of conditional invariance for boundary value problems involving a wide range of boundary conditions (including initial value problems as a special case) is proposed. It is shown that other definitions worked out in order to…