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We introduce a numerical variational method based on the Rayleigh-Ritz optimization principle for predicting two-dimensional self-trapped beams in nonlinear media. This technique overcomes the limitation of the traditional variational…
This paper deals the implementation of \emph{homotopy perturbation transform method} (HPTM) for numerical computation of initial valued autonomous system of time-fractional partial differential equations (TFPDEs) with proportional delay,…
A characteristic feature of differential-algebraic equations is that one needs to find derivatives of some of their equations with respect to time, as part of so called index reduction or regularisation, to prepare them for numerical…
Probabilistic sampling methods have become very popular to solve single-shot path planning problems. Rapidly-exploring Random Trees (RRTs) in particular have been shown to be efficient in solving high dimensional problems. Even though…
Recently, a new fractional derivative called the conformable fractional derivative is given which is based on the basic limit definition of the derivative in [1]. Then, the fractional versions of chain rules, exponential functions,…
Partial Differential Equations (PDEs) are central to science and engineering. Since solving them is computationally expensive, a lot of effort has been put into approximating their solution operator via both traditional and recently…
In this paper, we propose a direct solution method for optimal switching problems of one-dimensional diffusions. This method is free from conjectures about the form of the value function and switching strategies, or does not require the…
Polytopal methods provide a flexible framework for the numerical approximation of partial differential equations on general meshes. Their convergence analysis raises specific challenges due to their inherently non-conforming nature and, in…
In this study linear and nonlinear higher order singularly perturbed problems are examined by a numerical approach, the differential quadrature method. Here, the main idea is using Chebyshev polynomials to acquire the weighting coefficient…
We present a new method for the numerical solution of the radiative-transfer equation (RTE) in multidimensional scenarios commonly encountered in computational astrophysics. The method is based on the direct solution of the Boltzmann…
A singularly perturbed linear system of second order ordinary differential equations of reaction-diffusion type with given boundary conditions is considered. The leading term of each equation is multiplied by a small positive parameter.…
We are interested in finding a solution to the tensor complementarity problem with a strong M-tensor, which we call the M-tensor complementarity problem. We propose a lower dimensional linear equation approach to solve that problem. At each…
We introduce DDE-Solver, a Maple package designed for solving Discrete Differential Equations (DDEs). These equations are functional equations relating algebraically a formal power series F(t, u) with polynomial coefficients in a…
In this paper, we study the linear transport model by adopting the deep learning method, in particular the deep neural network (DNN) approach. While the interest of using DNN to study partial differential equations is arising, here we adapt…
This paper proposes a deep-learning-based domain decomposition method (DeepDDM), which leverages deep neural networks (DNN) to discretize the subproblems divided by domain decomposition methods (DDM) for solving partial differential…
In this paper, we present numerical procedures to compute solutions of partial differential equations posed on fractals. In particular, we consider the strong form of the equation using standard graph Laplacian matrices and also weak forms…
A version of the Dynamical Systems Method (DSM) for solving ill-conditioned linear algebraic systems is studied in this paper. An {\it a priori} and {\it a posteriori} stopping rules are justified. An algorithm for computing the solution…
There are two usual computational methods for linear (waves and instabilities) problem: eigenvalue (dispersion relation) solver and initial value solver. In fact, we can introduce an idea of the combination of them, i.e., we keep time…
In this short note we are presenting a method of finding particular solutions of nonhomegeneous linear equations. This approach is different from methods of undetermined coefficients or variation of parameters presented in virtually every…
Symmetry is a powerful tool for finding analytical solutions to differential equations, both partial and ordinary, via the similarity variables or via the invariance of the equation under group transformations. It is the largest group of…