Related papers: Numerical Solution for a Class of Evolution Differ…
In this paper we present an error analysis of an Eulerian finite element method for solving parabolic partial differential equations posed on evolving hypersurfaces in $\mathbb{R}^d$, $d=2,3$. The method employs discontinuous piecewise…
In this article, we study the following fractional $p$-Laplacian equation with critical growth singular nonlinearity \begin{equation*} \quad (-\De_{p})^s u = \la u^{-q} + u^{\alpha}, u>0 \; \text{in}\; \Om,\quad u = 0 \; \mbox{in}\; \mb R^n…
A new method of numerical solution for partial differential equations is proposed. The method is based on a fast matrix multiplication algorithm. Two-dimensional Poison equation is used for comparison of the proposed method with…
In this note we develop a numerical method for partial differential equations with changing type. Our method is based on a unified solution theory found by Rainer Picard for several linear equations from mathematical physics. Parallel to…
We study solution techniques for parabolic equations with fractional diffusion and Caputo fractional time derivative, the latter being discretized and analyzed in a general Hilbert space setting. The spatial fractional diffusion is realized…
The accurate numerical solution of partial differential equations is a central task in numerical analysis allowing to model a wide range of natural phenomena by employing specialized solvers depending on the scenario of application. Here,…
We investigate a scalar partial differential equation model for the formation of biological transportation networks. Starting from a discrete graph-based formulation on equilateral triangulations, we rigorously derive the corresponding…
We study regularity properties of solutions to nonlinear and nonlocal evolution problems driven by the so-called \emph{$0$-order fractional $p-$Laplacian} type operators: $$ \partial_t u(x,t)=\mathcal{J}_p u(x,t):=\int_{\mathbb{R}^n}…
We investigate existence and uniqueness of solutions for a class of nonlinear nonlocal problems involving the fractional $p$-Laplacian operator and singular nonlinearities.
This paper is concerned with the analysis of a new stable space-time finite element method (FEM) for the numerical solution of parabolic evolution problems in moving spatial computational domains. The discrete bilinear form is elliptic on…
We study numerical methods for solving a system of quasilinear stochastic partial differential equations known as the stochastic Landau-Lifshitz-Bloch (LLB) equation on a bounded domain in $\mathbb R^d$ for $d=1,2$. Our main results are…
In this paper we propose an algorithm for the numerical solution of arbitrary differential equations of fractional order. The algorithm is obtained by using the following decomposition of the differential equation into a system of…
The paper introduces a new finite element numerical method for the solution of partial differential equations on evolving domains. The approach uses a completely Eulerian description of the domain motion. The physical domain is embedded in…
We consider a saddle point formulation for a sixth order partial differential equation and its finite element approximation, for two sets of boundary conditions. We follow the Ciarlet-Raviart formulation for the biharmonic problem to…
In this paper, we consider the nonlinear equation involving the fractional p-Laplacian with sign-changing potential. This model draws inspiration from De Giorgi Conjecture. There are two main results in this paper. Firstly, we obtain that…
In this note, we present a new numerical method for solving backward stochastic differential equations. Our method can be viewed as an analogue of the classical finite element method solving deterministic partial differential equations.
Let $p,q$ be functions on $\mathbb{R}^{N}$ satisfying $1\ll q\ll p\ll N$, we consider $p(x)$-Laplacian problems of the form \[ \left\{ \begin{array} [c]{l}% -\Delta_{p(x)}u+V(x)\vert u\vert ^{p(x)-2}u=\lambda\vert u\vert…
The paper develops the method for construction of families of particular solutions to some classes of nonlinear Partial Differential Equations (PDE). Method is based on the specific link between algebraic matrix equations and PDE.…
We consider systems of stochastic evolutionary equations of the $p$-Laplace type. We establish convergence rates for a finite-element based space-time approximation, where the error is measured in a suitable quasi-norm. Under natural…
The systems of nonlinear Volterra integral equations of the first kind with jump discontinuous kernels are studied. The iterative numerical method for such nonlinear systems is proposed. Proposed method employs the modified…