Hyperbolic partial differential equation ≈ Hyperbolic partial differential equation
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LIMITATIONS OF PHYSICS INFORMED MACHINE LEARNING FOR NONLINEAR TWO-PHASE TRANSPORT IN POROUS MEDIA Open
Deep learning techniques have recently been applied to a wide range of computational physics problems. In this paper, we focus on developing a physics-based approach that enables the neural network to learn the solution of a dynamic fluid-…
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New Complex Hyperbolic Structures to the Lonngren-Wave Equation by Using Sine-Gordon Expansion Method Open
In this paper, a powerful sine-Gordon expansion method (SGEM) with aid of a computational program is used in constructing a new hyperbolic function solutions to one of the popular nonlinear evolution equations that arises in the field of m…
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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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Significant Production of Thermal Energy in Partially Ionized Hyperbolic Tangent Material Based on Ternary Hybrid Nanomaterials Open
Nanoparticles are frequently used to enhance the thermal performance of numerous materials. This study has many practical applications for activities that have to minimize losses of energy due to several impacts. This study investigates th…
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Degenerate Parabolic Stochastic Partial Differential Equations: Quasilinear case Open
In this paper, we study the Cauchy problem for a quasilinear degenerate parabolic stochastic partial differential equation driven by a cylindrical Wiener process. In particular, we adapt the notion of kinetic formulation and kinetic soluti…
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Clawpack: building an open source ecosystem for solving hyperbolic PDEs Open
Clawpack is a software package designed to solve nonlinear hyperbolic partial differential equations using high-resolution finite volume methods based on Riemann solvers and limiters. The package includes a number of variants aimed at diff…
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On the exact soliton solutions and different wave structures to the (2+1) dimensional Chaffee–Infante equation Open
Nonlinear phenomena observed in diverse scientific disciplines, including fluid dynamics, plasma physics, and biology, are frequently described by partial differential equations (PDEs). Among these PDEs, the Chaffee–Infante equation holds …
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Application of modified exp-function method for strain wave equation for finding analytical solutions Open
The strain wave equation in micro-structured solids, which is significant in solid physics, is offered for consideration in this work. This is accomplished using the modified exp-function method, which is one of the most powerful ways for …
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New Complex and Hyperbolic Forms for Ablowitz–Kaup–Newell–Segur Wave Equation with Fourth Order Open
Researching different solutions of nonlinear models has been interesting in different fields of science and application. In this study, we investigated different solutions of fourth-order nonlinear Ablowitz– Kaup–Newell–Segur wave equation…
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Exact and explicit travelling-wave solutions to the family of new 3D fractional WBBM equations in mathematical physics Open
In this paper, the new 3D fractional Wazwaz-Benjamin-Bona-Mahony (WBBM) equations newly announced are investigated with the introduction of the spatial and sequential fractional-order derivatives expending in the sense of conformable deriv…
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Novel Complex Wave Solutions of the (2+1)-Dimensional Hyperbolic Nonlinear Schrödinger Equation Open
This manuscript focuses on the application of the (m+1/G′)-expansion method to the (2+1)-dimensional hyperbolic nonlinear Schrödinger equation. With the help of projected method, the periodic and singular complex wave solutions to the cons…
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HYPERBOLIC TYPE SOLUTIONS FOR THE COUPLE BOITI-LEON-PEMPINELLI SYSTEM Open
In this paper, the (1/G')-expansion method is used to solve the coupled Boiti-Leon-Pempinelli (CBLP) system. The proposed method was used to construct hyperbolic type solutions of the nonlinear evolution equations. To asses the applicabili…
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Exact traveling wave solutions for (2+1)-dimensional Konopelchenko-Dubrovsky equation by using the hyperbolic trigonometric functions methods Open
In this research, the extended rational sinh-cosh method and the modified extended tanh-function method for mathematically constructing traveling wave solutions to the (2+1)-dimensional integro-differential Konopelchenko-Dubrovsky evolutio…
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Unique Solvability of a Boundary Value Problem for a Loaded Fractional Parabolic-Hyperbolic Equation with Nonlinear Terms Open
This work is devoted to study the existence and uniqueness of solution of an analogue of the Gellerstedt problem with nonlocal assumptions on the boundary and integral gluing conditions for the parabolic-hyperbolic type equation with nonli…
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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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On High Order ADER Discontinuous Galerkin Schemes for First Order Hyperbolic Reformulations of Nonlinear Dispersive Systems Open
This paper is on arbitrary high order fully discrete one-step ADER discontinuous Galerkin schemes with subcell finite volume limiters applied to a new class of first order hyperbolic reformulations of nonlinear dispersive systems based on …
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Efficient Implementation of ADER Discontinuous Galerkin Schemes for a Scalable Hyperbolic PDE Engine Open
In this paper we discuss a new and very efficient implementation of high order accurate arbitrary high order schemes using derivatives discontinuous Galerkin (ADER-DG) finite element schemes on modern massively parallel supercomputers. The…
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Necessary and Sufficient Conditions on the Exponential Stability of Positive Hyperbolic Systems Open
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An efficient hyperbolic relaxation system for dispersive non-hydrostatic water waves and its solution with high order discontinuous Galerkin schemes Open
In this paper we propose a novel set of first-order hyperbolic equations that can model dispersive non-hydrostatic free surface flows. The governing PDE system is obtained via a hyperbolic approximation of the family of non-hydrostatic fre…
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Constructions of solitary travelling wave solutions for Ito integro-differential equation arising in plasma physics Open
Constructing exact and numerical solutions of partial differential equations (PDEs) has become an active area in recent years. This work focuses on developing new exact and numerical solutions for (1+1)- dimensional Ito integro-differentia…
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Operational Approach and Solutions of Hyperbolic Heat Conduction Equations Open
We studied physical problems related to heat transport and the corresponding differential equations, which describe a wider range of physical processes. The operational method was employed to construct particular solutions for them. Invers…
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Consistent travelling waves solutions to the non-linear time fractional Klein–Gordon and Sine-Gordon equations through extended tanh-function approach Open
In this study, the extended tanh-function method has been used to find further general travelling wave solutions for space-time fractional nonlinear partial differential equations, namely, the time fractional nonlinear Sine-Gordon equation…
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A Novel Robust Strategy for Discontinuous Galerkin Methods in Computational Fluid Mechanics: Why? When? What? Where? Open
In this paper we will review a recent emerging paradigm shift in the construction and analysis of high order Discontinuous Galerkin methods applied to approximate solutions of hyperbolic or mixed hyperbolic-parabolic partial differential e…
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Exact wave solutions to the simplified modified Camassa-Holm equation in mathematical physics Open
In this article, we consider the exact solutions to the simplified modified Camassa-Holm (SMCH) equation which has many potential applications in mathematical physics and engineering sciences. We examine the exact travelling wave solutions…
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Analysis of the SBP-SAT Stabilization for Finite Element Methods Part I: Linear Problems Open
In the hyperbolic community, discontinuous Galerkin (DG) approaches are mainly applied when finite element methods are considered. As the name suggested, the DG framework allows a discontinuity at the element interfaces, which seems for ma…
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Analytical Solution of Fractional-Order Hyperbolic Telegraph Equation, Using Natural Transform Decomposition Method Open
In the current paper, fractional-order hyperbolic telegraph equations are considered for analytical solutions, using the decomposition method based on natural transformation. The fractional derivative is defined by the Caputo operator. The…
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A reduction technique to solve the generalized nonlinear dispersive mK(m,n) equation with new local derivative Open
In this work, we consider the generalized nonlinear dispersive mK(m,n) equation with a recently defined local derivative in the temporal direction. Different types of exact solutions are extracted by Nucci’s reduction technique. Combinatio…
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Solutions of fractional order pseudo-hyperbolic telegraph partial differential equations using finite difference method Open
In this study, the explicit finite difference method is used to solve the fractional-order pseudo-hyperbolic telegraph partial differential equation by means of Caputo fractional derivative. A first-order finite difference approach is cons…
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Minimum Time Problem for <i>n×n</i> Co-operative Hyperbolic Lag Systems Open
In this paper, a minimum time problem for n×n co-operative hyperbolic systems involving Laplace operator and with time-delay is considered. First, the existence of a unique solution of such hyperbolic system with time-delay is proved. Then…