Related papers: Approximate solution to the fractional Lane-Emden …
We use a numerical-analytic technique to construct a sequence of successive approximations to the solution of a system of fractional differential equations, subject to Dirichlet boundary conditions. We prove the uniform convergence of the…
We extend the piecewise orthogonal collocation method to computing periodic solutions of coupled renewal and delay differential equations. Through a rigorous error analysis, we prove convergence of the relevant finite-element method and…
In this article, we introduce a finite element method designed for the robust computation of approximate signed distance functions to arbitrary boundaries in two and three dimensions. Our method employs a novel prediction-correction…
Fractional differential equations (FDEs) describe subdiffusion behavior of dynamical systems. Its non-local structure requires taking into account the whole evolution history during the time integration, which then possibly causes…
A method for the numerical solution of variable order (VO) fractional differential equations (FDE) is presented. The method applies to linear as well as to nonlinear VO-FDEs. The Caputo type VO fractional derivative is employed. First, an…
We study the finite element approximation of linear second-order elliptic partial differential equations in nondivergence form with highly heterogeneous diffusion and drift coefficients. A generalized Cordes condition is imposed to…
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 relations between solutions of the three types of totally linear partial differential equations of first order are presented. The approach is based on factorization of a non-homogeneous first order differential operator to products…
We present a simple systematic algorithm for construction of expansions of the solutions of ordinary differential equations with rational coefficients in terms of mathematical functions having indefinite integral representation. The…
This letter aims at resolving the issues raised in the recent short communication [1] and answered by [2] by proposing a systematic approximation scheme based on non-mapped shape functions, which both allows to fully exploit the unique…
Many problems in machine learning can be solved by rounding the solution of an appropriate linear program (LP). This paper shows that we can recover solutions of comparable quality by rounding an approximate LP solution instead of the ex-…
The recently developed theory of quasi-Lie schemes is studied and applied to investigate several equations of Emden type and a scheme to deal with them and some of their generalisations is given. As a first result we obtain t-dependent…
In this paper, we derive an asymptotic error expansion for the eigenvalue approximations by the lowest order Raviart-Thomas mixed finite element method for the general second order elliptic eigenvalue problems. Extrapolation based on such…
We address composite optimization problems, which consist in minimizing the sum of a smooth and a merely lower semicontinuous function, without any convexity assumptions. Numerical solutions of these problems can be obtained by proximal…
We prove the existence, uniqueness, and sharp bilateral pointwise estimates for positive bounded solutions to the Lane--Emden type problem \[ \begin{cases} L u = \sum\limits_{i=1}^{m}\sigma_{i} u^{q_{i}}+\sigma_0, \quad u\geq0 & \text{in }…
This paper deals with the solution of large classes of systems of nonlinear partial differential equations (PDEs) in spaces of generalized functions that are constructed as the completion of uniform convergence spaces. The existence result…
Fractional diffusion has become a fundamental tool for the modeling of multiscale and heterogeneous phenomena. However, due to its nonlocal nature, its accurate numerical approximation is delicate. We survey our research program on the…
The standard mixed finite element approximations of Hodge Laplace problems associated with the de Rham complex are based on proper discrete subcomplexes. As a consequence, the exterior derivatives, which are local operators, are computed…
The work in this paper is four-fold. Firstly, we introduce an alternative approach to solve fractional ordinary differential equations as an expected value of a random time process. Using the latter, we present an interesting numerical…
This paper presents analytical-approximate solutions of the time-fractional Cahn-Hilliard (TFCH) equations of fourth and sixth-order using the new iterative method (NIM) and q-homotopy analysis method (q-HAM). We obtained convergent series…