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In this work we apply the Adomian decomposition method combined with the Laplace transform (LADM) in order to solve the 1-dimensional nonlinear Schrodinger equation whose nonlinear term presents a nonlinear defocusing strength that varies…
In this work, we present a semi-numerical solution of a fractal telegraphic dual-porosity fluid flow model. It combines Laplace transform and finite difference schemes. The Laplace transform handles the time variable whereas the finite…
Far as we know there are not exact solutions to the equation of motion for a relativistic harmonic oscillator. In this paper, the relativistic harmonic oscillator equation which is a nonlinear ordinary differential equation is studied by…
This paper is presented to give numerical solutions of some cases of nonlinear wave-like equations with variable coefficients by using Reduced Differential Transform Method (RDTM). RDTM can be applied most of the physical, engineering,…
The modeling of many phenomena in various fields such as mathematics, physics, chemistry, engineering, biology, and astronomy is done by the nonlinear partial differential equations (PDE). The hyperbolic telegraph equation is one of them,…
The Kundu-Eckhaus equation is a nonlinear partial differential equation which seems in the quantum field theory, weakly nonlinear dispersive water waves and nonlinear optics. In spite of its importance, exact solution to this nonlinear…
The Lattice Boltzmann Method (LBM), e.g. in [ 1] and [2 ], can be interpreted as an alternative method for the numerical solution of partial differential equations. Consequently, although the LBM is usually applied to solve fluid flows, the…
The present article is devoted to developing the Legendre wavelet operational matrix method (LWOMM) to find the numerical solution of two-dimensional hyperbolic telegraph equations (HTE) with appropriate initial time boundary space…
Quantum scientific computing is to solve engineering and science problems such as simulation and optimization on quantum computers. Solving ordinary and partial differential equations (PDEs) is essential in simulations. However, existing…
We consider a class of integer-constrained optimization problems governed by partial differential equation (PDE) constraints and regularized via total variation (TV) in the context of topology optimization. The presence of discrete design…
The standard methodology handling nonlinear PDE's involves the two steps: numerical discretization to get a set of nonlinear algebraic equations, and then the application of the Newton iterative linearization or its variants to solve the…
Reduced Differental Transform Method (RDTM) which is one of the useful and effective numerical approximate method is applied to solve nonlinear time-dependent Foam Drainage Equation (FDE). Also, we compared the presented method with the…
A nonlocal form of a two-layer fluid system is proposed by a simple symmetry reduction, then by applying multiple scale method to it a general nonlocal two place variable coefficient modified KdV (VCmKdV) equation with shifted space and…
A method for solving model nonlinear equations describing plasma oscillations in the presence of viscosity and resistivity is given. By first going to the Lagrangian variables and then transforming the space variable conveniently, the…
In this paper, we solve Laplace equation analytically by using differential transform method. For this purpose, we consider four models with two Dirichlet and two Neumann boundary conditions and obtain the corresponding exact solutions. The…
An algorithm is proposed to implement unsteady jump boundary conditions, presenting discontinuity in physical quantities, within the lattice Boltzmann method (LBM). This is useful to tackle problems involving mass or heat transfer through…
This paper focuses on the numerical solution of a dual-phase-lag heat conduction equation on a space unbounded domain. First, based on the Laplace transform and the Pad\'e approximation, a high-order local artificial boundary condition is…
The biharmonic equation, as well as its nonlinear and inhomogeneous generalizations, plays an important role in engineering and physics. In particular the focusing biharmonic nonlinear Schr\"{o}dinger equation, and its standing wave…
We propose an approach to solve the stochastic neutron point kinetics equations using an adaptation of the diagonalization-decomposition method (DDM). This new approach (Double-DDM) yields a nonstiff solution for the stochastic formulation,…
We extend our previous work [F. Henr'iquez and J. S. Hesthaven, arXiv:2403.02847 (2024)] to the linear, second-order wave equation in bounded domains. This technique uses two widely known mathematical tools to construct a fast and efficient…