Related papers: Approximate Q-conditional symmetries of partial di…
In this article we develop a new methodology to prove weak approximation results for general stochastic differential equations. Instead of using a partial differential equation approach as is usually done for diffusions, the approach…
This paper investigates quenching solutions of an one-dimensional, two-sided Riemann-Liouville fractional order convection-diffusion problem. Fractional order spatial derivatives are discretized using weighted averaging approximations in…
We obtain approximate convexity principles for solutions to some classes of nonlinear elliptic partial differential equations in convex domains involving approximately concave nonlinearities. Furthermore, we provide some applications to…
We study invariant solutions of a certain class of time-fractional diffusion-wave equations with variable coefficients via Lie symmetry analysis. In physics, the fractional diffusion equation describes transport dynamics that are governed…
We propose an approximation scheme for a class of semilinear parabolic equations that are convex and coercive in their gradients. Such equations arise often in pricing and portfolio management in incomplete markets and, more broadly, are…
We consider strong convergence of the finite differences approximation in space for stochastic reaction diffusion equations with multiplicative noise under a one-sided Lipschitz condition only. We derive convergence with an implicit rate…
The theory of quasi-Lie systems, i.e. systems of first order ordinary differential equations which can be related via a generalised flow to Lie systems, is extended to systems of partial differential equations and its applications to…
We have solved completely the problem of the description of quasi-linear hyperbolic differential equations in two independent variables that are invariant under three-parameter Lie groups.
In this note we analyse \emph{quantitative} approximation properties of a certain class of \emph{nonlocal} equations: Viewing the fractional heat equation as a model problem, which involves both \emph{local} and \emph{nonlocal}…
We study an approximation method to solve nonlinear multi-term fractional differential equations with initial conditions or boundary conditions. First, we transform the nonlinear multi-term fractional differential equations with initial…
We analyze some exact and approximate solutions to nonlinear equations for heat transfer models. We prove that recent results derived from a method based on Lie algebras are either trivial or wrong. We test a simple analytical expression…
We perform a detailed Lie symmetry analysis for the hyperbolic system of partial differential equations that describe the one-dimensional Shallow Water magnetohydrodynamics equations within a rotating reference frame. We consider a relaxing…
Using Lie symmetry methods for differential equations we have investigated the symmetries of a Lagrangian for a plane symmetric static spacetime. Perturbing this Lagrangian we explore its approximate symmetries. It has a non-trivial…
We propose a theorem that extends the classical Lie approach to the case of fractional partial differential equations (fPDEs) of the Riemann--Liouville type in (1+1) dimensions.
A class of nonlinear reaction-diffusion-convection equations describing various processes in physics, biology, chemistry etc. is under study in the case of time and two space variables. The group of equivalence transformations is…
Symmetry properties of PDE's are considered within a systematic and unifying scheme: particular attention is devoted to the notion of conditional symmetry, leading to the distinction and a precise characterization of the notions of ``true''…
In this paper, we consider the approximate controllability of partial differential equations with time derivatives of non-integer order via boundary control. We first show the unique existence of the solution under smooth boundary…
A large system of ordinary differential equations is approximated by a parabolic partial differential equation with dynamic boundary condition and a different one with Robin boundary condition. Using the theory of differential operators…
We exhaustively classify the Lie reductions of the real dispersionless Nizhnik equation to partial differential equations in two independent variables and to ordinary differential equations. Lie and point symmetries of reduced equations are…
The notion of the characteristic Lie algebra of the discrete hyperbolic type equation is introduced. An effective algorithm to compute the algebra for the equation given is suggested. Examples and further applications are discussed.