First Integral
The First Integral Method for Solving Maccari’s System
... The first integral method was first proposed for solving Burger-KdV equation [1] which is based on the ring theory of commutative ...the first time the applicability and effectiveness of the ...
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Exact solutions of the 2D Ginzburg-Landau equation by the first integral method
... The remainder of this paper is organized as follows. In Section 2, using the first- integral method which is based on the ring theory of commutative algebra, we es- tablish the exact travelling wave ...
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EXACT TRAVELLING WAVE SOLUTIONS FOR MANAKOV SYSTEM BY USING FIRST INTEGRAL METHOD
... the first integral method for finding new forms for the exact solutions of nonlinear coupled one- dimensional partial differential equations of Manakov ...the first integral method is an ...
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Programming First Integral Method General Formula for the Solving Linear and Nonlinear Equations
... the first integral method is used to find the actual solution of equations in a simple way, rather than the ex-complicated ...of first integral method makes the solution more available and ...
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New Exact Explicit Solutions of the Generalized Zakharov Equation via the First Integral Method
... the first integral method, in the form of trigonometric and exponential ...the first integral method is an efficient way to solve the coupled nonlinear equations and get rich explicit ...
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Solitary Wave solutions of the BK equation and ALWW system by using the first integral method
... In this present work we have presented a number of solitary wave solutions to the Broer-Kaup equations and approximate long water wave equations. The first integral method is a very powerful method for finding exact ...
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Exact solutions of two nonlinear partial differential equations by using the first integral method
... first integral method, which is based on the ring theory of commuta- tive algebra, due to Feng [–] has been applied by many authors to solve different types of nonlinear equations in science and engineering ...
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Spectral cluster bounds for orthonormal systems and oscillatory integral operators in Schatten spaces
... This article is organized as follows. In Section 1, we prove bounds on oscillatory integral operators for orthonormal functions. In Section 2, we apply these results to prove the generalization (6) of Sogge’s ...
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A solution for Volterra Integral Equations of the First Kind Based on Bernstein Polynomials
... the integral equation will be ...the first kind Fredholm integral equations ...Fredholm integral equations of the first kind via piecewise interpolation is ...solve first kind ...
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A Survey of Regularization Methods of Solution of Volterra Integral Equations of the First Kind
... for first kind Volterra integral equations that maintain the Volterra structure, we never lost sight of the distinguishing features associated with this class of equations, which reflect in the uncertainty ...
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Dropped Ball Travel Time using Variation and Integration
... If 𝑏 = 𝑥 is identified with the current variable, the equation is known as the Volterra equation. , 𝑎 𝑎𝑛𝑑 𝑏 are constant. 𝐾(𝑥, 𝜀) is known as the kernel. The integral equation is said to be of the first ...
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The Combined Reproducing Kernel Method and Taylor Series for Handling Fractional Differential Equations
... nonsingular integral equations in the reproducing kernel Hilbert space which was pre- sented by Zaremba in ...gular integral equations with cosecant kernel [25], Fredholm integral equation of the ...
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Unified Integrals about Certain Gimel-Function
... In this paper two finite integrals involving the generalized multivariable function noted presented here and a general polynomial having arguments of the type have been evaluated. These integrals, besides being of very ...
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Regularization and Adaptation for the Approximation of Nonsmooth Solutions for Fredgolm First Kind Integral Equations
... The field of inverse problems is of large interest due to the importance of applications to science and industry. Since most inverse problems cannot be solved analyti- cally, computational methods play a fundamental role. ...
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Numerical solution of two-dimensional integral equations of the first kind by multi-step methods
... the integral equations of the first kind are ill-posed problems, that is, a small perturbation in the given data makes a large perturbation in the solution ...Volterra-Fredholm integral equations ...
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EVALUATION OF SOME NON-ELEMENTARY INTEGRALS INVOLVING SINE, COSINE, EXPONENTIAL AND LOGARITHMIC INTEGRALS: PART II
... applied to the solution of Milne’s integral equations [2], there are also used in modeling radiative transfer processes in the atmosphere and in nuclear reactors [10], etc. Exponential asymptotics involving ...
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Approximate solution of the Fredholm integral equation of the first kind in a reproducing kernel Hilbert space
... In this work, we wish to solve the Fredholm integral equation of the first kind in RKHS. The work is organized as follows. A RKHS W 2 1 [ a , b ] is introduced in Section 2. The representation of solutions ...
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Approximate solution of a system of singular integral equations of the first kind by using Chebyshev polynomials
... Studies on this singular integral equation can be found in some literatures (see [1,3,6,7]). Chakrabarti and Berghe [3] proposed a method for solving (2), using polynomial approximation and collocation points have ...
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Sinc Nyström method for a class of nonlinear Volterra integral equations of the first kind
... Volterra integral equations of the first kind arise in many fields of science and engineering, for example, in diffusion problems, fluid dynamics, heat conduction problems, nonlinear dynamic systems identification, ...
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EVALUATION OF SOME NON-ELEMENTARY INTEGRALS INVOLVING SINE, COSINE, EXPONENTIAL AND LOGARITHMIC INTEGRALS: PART I
... Definition 1. An elementary function is a function of one variable constructed using that variable and constants, and by performing a finite number of repeated algebraic operations involving exponentials and logarithms. ...
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