Solving Strongly Nonlinear Oscillators by New Numerical Method

Batiha, Belal; Ghanim, F.

doi:10.12732/ijpam.v116i1.11

Cited by 4 publications

(5 citation statements)

References 16 publications

(22 reference statements)

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“…This section provides an outline of the NIM numerical method, detailing its approach as follows [27][28][29][30]:…”

Section: Overview Of the Nimmentioning

confidence: 99%

“…Thus, where 2 presents the comparison between the 1-iteration of NIM and the exact solution defined by Equation (27).…”

Section: Examination Of the Pkp Equation With Numerical Applicationsmentioning

confidence: 99%

“…Table 3 displays a contrast between the initial iteration of NIM and the exact solution defined by Equation (27).…”

Section: Examination Of the Pkp Equation With Numerical Applicationsmentioning

confidence: 99%

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Innovative Solutions for the Kadomtsev–Petviashvili Equation via the New Iterative Method

Batiha

2024

Mathematical Problems in Engineering

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This research paper presents a new iterative method (NIM) for obtaining the solution to the potential Kadomtsev–Petviashvili (PKP) equation. NIM is a promising approach to solving complex mathematical problems, and its effectiveness and efficiency are highlighted through its application to the PKP equation. The results obtained through the use of NIM are compared to the exact solutions of the PKP equation, and it is found that the NIM approach provides results that are in close agreement with the exact solutions. This demonstrates the utility and accuracy of NIM and makes it a valuable tool for solving similar mathematical problems in the future. Furthermore, the lack of discretization in the NIM approach makes it a more convenient method for solving the PKP equation compared to traditional approaches that require discretization. Overall, the findings of this research paper suggest that NIM is a highly effective and convenient method for obtaining approximate analytical solutions to complex mathematical problems, such as the 2+1-dimensional PKP equation.

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“…This section provides an outline of the NIM numerical method, detailing its approach as follows [27][28][29][30]:…”

Section: Overview Of the Nimmentioning

confidence: 99%

“…Thus, where 2 presents the comparison between the 1-iteration of NIM and the exact solution defined by Equation (27).…”

Section: Examination Of the Pkp Equation With Numerical Applicationsmentioning

confidence: 99%

See 1 more Smart Citation

Innovative Solutions for the Kadomtsev–Petviashvili Equation via the New Iterative Method

Batiha

2024

Mathematical Problems in Engineering

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“…The RDE is named after the name of Italian nobleman Count Jacopo Francesco Riccati(1676-1754) [4]. In the field of applied science and engineering, the RDEs have played an essential role [2][3][4][5][6][7]29]. A one dimensional static Schrodinger equation is closely related to RDEs.…”

Section: Introductionmentioning

confidence: 99%

“…Satisfying projective Riccati equations, solitary wave solutions of nonlinear partial differential equations can be expressed as polynomials in two elementary functions [4,7]. In some control theory problems such as dynamic games, linear system with Markovian jumps and stochastic controls RDEs act predominantly [7,29]. Apart from these applications RDEs is also used in stochastic realization theory, robust stabilization, and network synthesis and presently in financial mathematics [4].…”

Section: Introductionmentioning

confidence: 99%

Newton-Raphson based modified Laplace Adomian decomposition method for solving quadratic Riccati differential equations

Mishra

Rani

2016

MATEC Web of Conferences

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Abstract. Numerical Laplace transform method is applied to approximate the solution of nonlinear (quadratic) Riccati differential equations mingled with Adomian decomposition method. A new technique is proposed in this work by reintroducing the unknown function in Adomian polynomial with that of well known NewtonRaphson formula. The solutions obtained by the iterative algorithm are exhibited in an infinite series. The simplicity and efficacy of method is manifested with some examples in which comparisons are made among the exact solutions, ADM (Adomian decomposition method), HPM (Homotopy perturbation method), Taylor series method and the proposed scheme.

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Application of the New Iterative Method (NIM) to the Generalized Burgers–Huxley Equation

2023

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In this paper, we propose the new iterative method (NIM) for solving the generalized Burgers–Huxley equation. NIM provides an approximate solution without the need for discretization and is based on a set of iterative equations. We compared the NIM with other established methods, such as Variational Iteration Method (VIM), Adomian Decomposition Method (ADM), and the exact solution, and found that it is efficient and easy to use. NIM has the advantage of quick convergence, easy implementation, and handling of a wide range of initial conditions. The comparison of the present symmetrical results with the existing literature is satisfactory.

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Solving Strongly Nonlinear Oscillators by New Numerical Method

Abstract: and Runge-Kutta method in order to prove the accuracy of DJM.

Cited by 4 publications

References 16 publications

Innovative Solutions for the Kadomtsev–Petviashvili Equation via the New Iterative Method

Innovative Solutions for the Kadomtsev–Petviashvili Equation via the New Iterative Method

Newton-Raphson based modified Laplace Adomian decomposition method for solving quadratic Riccati differential equations

Application of the New Iterative Method (NIM) to the Generalized Burgers–Huxley Equation

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