Results 11 to 20 of about 145 (75)
An Integral Equation Formulation for Two-Phase Flow and Other Nonlinear Flow Problems Through Porous Media [PDF]
SPE Annual Technical Conference and Exhibition, 1990 ABSTRACT Many flow problems encountered in petroleum reservoir engineering are characterized by nonlinearities and are difficult to solve analytically. The concept of a relative mass flow rate function is used to arrive at an integral equation formulation for some of these nonlinear flow problems.
Zhongxiang Chen +2 more
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A new fourth-order integrable nonlinear equation: breather, rogue waves, other lump interaction phenomena, and conservation laws [PDF]
Advances in Difference Equations, 2021 AbstractIn this study, we investigate a new fourth-order integrable nonlinear equation. Firstly, by means of the efficient Hirota bilinear approach, we establish novel types of solutions which include breather, rogue, and three-wave solutions. Secondly, with the aid of Lie symmetry method, we report the invariance properties of the studied equation ...
Dumitru Baleanu +2 more
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Pramana, 2023 In this paper, we present a method of deriving extended Prelle-Singer method's quantifiers from Darboux Polynomials for third-order nonlinear ordinary differential equations. By knowing the Darboux polynomials and its cofactors, we extract the extended Prelle-Singer method's quantities without evaluating the Prelle-Singer method's determining equations.
R Mohanasubha, M Senthilvelan
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A Computational Technique for Solving Three-Dimensional Mixed Volterra–Fredholm Integral Equations
Fractal and Fractional, 2023 In this article, a novel and efficient approach based on Lucas polynomials is introduced for solving three-dimensional mixed Volterra–Fredholm integral equations for the two types (3D-MVFIEK2).
Amr M. S. Mahdy +3 more
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Exact solutions for the fractional differential equations by using the first integral method
Nonlinear Engineering, 2015 In this paper, we apply the first integral method to study the solutions of the nonlinear fractional modified Benjamin-Bona-Mahony equation, the nonlinear fractional modified Zakharov-Kuznetsov equation and the nonlinear fractional Whitham-Broer-
Aminikhah Hossein +2 more
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Non-Associative Structures and Their Applications in Differential Equations
Mathematics, 2023 This article establishes a connection between nonlinear DEs and linear PDEs on the one hand, and non-associative algebra structures on the other. Such a connection simplifies the formulation of many results of DEs and the methods of their solution.
Yakov Krasnov
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AIMS MathematicsPicard's three step iteration algorithm was one of the iteration algorithms that was recently shown to be faster than some other iterative algorithms in the existing literature.
Lale Cona
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A Simple Approach to Volterra-Fredholm Integral Equations [PDF]
Journal of Applied and Computational Mechanics, 2020 This paper suggests a simple analytical method for Volterra-Fredholm integral equations, the solution process is similar to that by variational-based analytical method, e.g., Ritz method, however, the method requires no establishment of the variational ...
Ji-Huan He
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Advances in Mathematical Physics, 2023 In this study, the Fredholm hypersingular integral equation of the first kind with a singular right-hand function on the interval −1,1 is solved. The discontinuous solution on the domain −1,1 is approximated by a piecewise polynomial, and a collocation ...
M. R. Elahi +3 more
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Positive Solutions for Coupled Nonlinear Fractional Differential Equations
Journal of Applied Mathematics, 2014 We consider the existence of positive solutions for a coupled system of nonlinear fractional differential equations with integral boundary values. Assume the nonlinear term is superlinear in one equation and sublinear in the other equation.
Wenning Liu, Xingjie Yan, Wei Qi
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