Method of characteristics ≈ Method of characteristics
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Dispersive long wave of nonlinear fractional Wu-Zhang system via a modified auxiliary equation method Open
In this paper, we examine a modified auxiliary equation method. We applied this novel method on Wu-Zhang system. This model used to describe (1 + 1)-dimensional dispersive long wave in two horizontal directions on shallow waters. This mode…
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Solving Partial Differential Equations Using Deep Learning and Physical Constraints Open
The various studies of partial differential equations (PDEs) are hot topics of mathematical research. Among them, solving PDEs is a very important and difficult task. Since many partial differential equations do not have analytical solutio…
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Harnack inequality for kinetic Fokker-Planck equations with rough coefficients and application to the Landau equation Open
31 pages, 4 figures.
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Reduced differential transform method for partial differential equations within local fractional derivative operators Open
The non-differentiable solution of the linear and non-linear partial differential equations on Cantor sets is implemented in this article. The reduced differential transform method is considered in the local fractional operator sense. The …
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Conformal and covariant Z4 formulation of the Einstein equations: Strongly hyperbolic first-order reduction and solution with discontinuous Galerkin schemes Open
We present a strongly hyperbolic first-order formulation of the Einstein\nequations based on the conformal and covariant Z4 system (CCZ4) with\nconstraint-violation damping, which we refer to as FO-CCZ4. As CCZ4, this\nformulation combines…
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Families of Travelling Waves Solutions for Fractional-Order Extended Shallow Water Wave Equations, Using an Innovative Analytical Method Open
In the present research article, an efficient analytical technique is applied for travelling waves solutions of fractional partial differential equations. The investigated problems are reduced to ordinary differential equations, by a varia…
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New Analytical Technique for Solving a System of Nonlinear Fractional Partial Differential Equations Open
This paper introduces a new analytical technique (NAT) for solving a system of nonlinear fractional partial differential equations (NFPDEs) in full general set. Moreover, the convergence and error analysis of the proposed technique is show…
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Investigation of Exact Solutions of Nonlinear Evolution Equations Using Unified Method Open
In this article, an analytical technique based on unified method is applied to investigate the exact solutions of non-linear homogeneous evolution partial differential equations. These partial differential equations are reduced to ordinary…
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A nonlocal problem for loaded partial differential equations of fourth order Open
A nonlocal problem for the fourth order system of loaded partial differential equations is considered. The questions of a existence unique solution of the considered problem and ways of its construction are investigated. The nonlocal probl…
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A Numerically Validated Approach to Modeling Water Hammer Phenomena Using Partial Differential Equations and Switched Differential-Algebraic Equations Open
Water distribution networks are susceptible to abrupt pressure fluctuations and spikes due to rapid adjustments in valve and pump settings. A common occurrence resulting from the sudden closure of a valve, known as water hammer, can potent…
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Implementation and Validation of a Free Open Source 1D Water Hammer Code Open
This paper presents a free code for calculating 1D hydraulic transients in liquid-filled piping. The transient of focus is the Water Hammer phenomenon which may arise due to e.g., sudden valve closure, pump start/stop etc. The method of so…
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Reduced differential transform method for solving time and space local fractional partial differential equations Open
We apply the new local fractional reduced differential transform method to obtain the solutions of some linear and nonlinear partial differential equations on Cantor set.The reported results are compared with the related solutions presente…
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Harnack inequality for kinetic Fokker-Planck equations with rough coefficients and application to the Landau equation Open
We extend the De Giorgi--Nash--Moser theory to a class of kinetic Fokker-Planck equations and deduce new results on the Landau-Coulomb equation. More precisely, we first study the H{ö}lder regularity and establish a Harnack inequality for …
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Modeling Transient Pipe Flow in Plastic Pipes with Modified Discrete Bubble Cavitation Model Open
Most of today’s water supply systems are based on plastic pipes. They are characterized by the retarded strain (RS) that takes place in the walls of these pipes. The occurrence of RS increases energy losses and leads to a different form of…
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Droplet dynamics on chemically heterogeneous substrates Open
Slow droplet motion on chemically heterogeneous substrates is considered analytically and numerically. We adopt the long-wave approximation which yields a single partial differential equation for the droplet height in time and space. A mat…
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New approach to the Lax‐Wendroff modified differential equation for linear and nonlinear advection Open
The paper presents an enhanced analysis of the Lax‐Wendroff difference scheme—up to the eighth‐order with respect to time and space derivatives—of the modified‐partial differential equation (MDE) of the constant‐wind‐speed advection equati…
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Applications of differential transformation method to solve systems of ordinary and partial differential equations Open
In this study, the numerical solutions of some systems of ordinary and partial differential equations have been analyzed by using the Differential Transformation Method (DTM) and compared with solutions of other numerical methods .This met…
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Delayed oscillator model of pressure relief valves with outlet piping Open
The system of a vessel and a direct spring operated pressure relief valve is extended by a downstream pipe. The presented mathematical model consisting of ordinary and partial differential equations can be transformed to a system of differ…
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Exact and Approximate Solutions for Linear and Nonlinear Partial Differential Equations via Laplace Residual Power Series Method Open
The Laplace residual power series method was introduced as an effective technique for finding exact and approximate series solutions to various kinds of differential equations. In this context, we utilize the Laplace residual power series …
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Numerical Solution of Three-Dimensional Transient Heat Conduction Equation in Cylindrical Coordinates Open
Heat equation is a partial differential equation used to describe the temperature distribution in a heat-conducting body. The implementation of a numerical solution method for heat equation can vary with the geometry of the body. In this s…
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A novel Elzaki transform homotopy perturbation method for solving time-fractional non-linear partial differential equations Open
This paper presents the solution of important types of non-linear time-fractional partial differential equations via the conformable Elzaki transform Homotopy perturbation method. We apply the proposed technique to solve four types of non-…
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An efficient numerical scheme for the study of equal width equation Open
In this work a new numerical scheme is proposed in which Haar wavelet method is coupled with finite difference scheme for the solution of a nonlinear partial differential equation. The scheme transforms the partial differential equation to…
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Selected Mathematical Models Describing Flow in Gas Pipelines Open
The main aim of simulation programs is to study the behavior of gas pipe networks in certain conditions. Solving a specified set of differential equations describing transient (unsteady) flow in a gas pipeline for the adopted parameters of…
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The exact solutions to the generalized (2+1)-dimensional nonlinear wave equation Open
Due to the importance of the nonlinear partial differential equations in applied physics and engineering, many mathematicians and physicists are interesting to the nonlinear partial differential equations. One of the main tasks of studying…
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A fuzzy solution of nonlinear partial differential equations Open
In this paper, the reduced differential transform method (RDTM) is applied to solve fuzzy nonlinear partial differential equations (PDEs). The solutions are considered as infinite series expansions which converge rapidly to the solutions. …
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Numerical Solution of First Order Ordinary Differential Equation by Using Runge-Kutta Method Open
In this paper, the classical fourth-order Runge-Kutta methodis presented for solving the first-order ordinary differential equation. First, the given solution domain is discretizedby using a uniform discretization grid point. Next by apply…
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Multiple positive solutions for nonlinear mixed fractional differential equation with p-Laplacian operator Open
In this article, multiple positive solutions are considered for nonlinear mixed fractional differential equations with a p-Laplacian operator. Using the Avery–Peterson fixed point theorem, we conclude to the existence of positive solutions…
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A discontinuous Galerkin time integration scheme for second order differential equations with applications to seismic wave propagation problems Open
In this work, we present a high-order Discontinuous Galerkin time integration scheme for second-order (in time) differential systems that typically arise from the space discretization of the elastodynamics equation. By rewriting the origin…
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Cell-average based neural network method for hyperbolic and parabolic partial differential equations Open
Motivated by finite volume scheme, a cell-average based neural network method is proposed. The method is based on the integral or weak formulation of partial differential equations. A simple feed forward network is forced to learn the solu…
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An Application of New Transform " Mahgoub Transform" to Partial Differential Equations Open
In this paper .The Mahgoub Transform of partial derivatives is derived, and its applicability demonstrated using five different partial differential equations. In this paper we find the particular solutions of these equations. The result r…