Regularized Solution of the Cauchy Problem in an Unbounded Domain

Juraev, Davron Aslonqulovich; Shokri, Ali; Marian, Daniela

doi:10.3390/sym14081682

Cited by 5 publications

(2 citation statements)

References 23 publications

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“…In last few years, approximate analytical techniques attract attention of many researchers to fnd the approximate solutions of nonlinear PDE's due to their simplicity and easy approach. Series of methods have been established by mathematicians and researchers such as the homotopy perturbation method (HPM) [18,19], homotopy analysis method (HAM) [20][21][22], variational iteration method (VIM) [23][24][25], Adomian decomposition method (ADM) [26][27][28], diferential transform method (DTM) [29][30][31], tanh method (THM) and extended tanh method [32][33][34], use of trigamma function [35], Catalan-type numbers [36], and polynomials [37][38][39]. Traveling wave solutions are also prominent techniques in fnding the closed form of solutions.…”

Section: Introductionmentioning

confidence: 99%

Comparison of Approximate Analytical and Numerical Solutions of the Allen Cahn Equation

Hussain,

Haq,

Shah

et al. 2024

International Journal of Differential Equations

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Allen Cahn (AC) equation is highly nonlinear due to the presence of cubic term and also very stiff; therefore, it is not easy to find its exact analytical solution in the closed form. In the present work, an approximate analytical solution of the AC equation has been investigated. Here, we used the variational iteration method (VIM) to find approximate analytical solution for AC equation. The obtained results are compared with the hyperbolic function solution and traveling wave solution. Results are also compared with the numerical solution obtained by using the finite difference method (FDM). Absolute error analysis tables are used to validate the series solution. A convergent series solution obtained by VIM is found to be in a good agreement with the analytical and numerical solutions.

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Section: Introductionmentioning

confidence: 99%

Comparison of Approximate Analytical and Numerical Solutions of the Allen Cahn Equation

Hussain,

Haq,

Shah

et al. 2024

International Journal of Differential Equations

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“…Similarly, Adee and Atabo [17] presented a two point linear multi-step method for solving similar problems as the ones considered in [7] and the present work, except that their method is non starting and they used a fourth order Runge-Kutta method in obtaining the starting values. In this work, our method is self-starting and does not rely on other methods to start (see also [18][19][20][21][22][23][24][25]. )…”

Section: Introductionmentioning

confidence: 99%

Comparing the Performance of Two Butcher-Based Block Hybrid Algorithms for the Solution of Initial Value Problems

Akinola,

Shokri,

Sunday

et al. 2024

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In this paper, we compare the performances of two Butcher-based block hybrid methods for the numerical integration of initial value problems. We compare the condition numbers of the linear system of equations arising from both methods and the absolute errors of the solution obtained. The results of the numerical experiments illustrate that the better conditioned method outperformed its less conditioned counterpart based on the absolute errors. In addition, after applying our method on some examples, it was discovered that the absolute errors in this work were better than those of a recent study in the literature. Hence, we recommend this method for the numerical solution of stiff and non-stiff initial value problems.

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Calculation algorithm for electromagnetic wave processes in multi-wire intersystem ETL

Huseyn,

Hashimov,

Shokri

et al. 2024

Discov Electron

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The nature of the transient process and the magnitude of the overvoltages are determined by a large number of factors in the HV/EHV AC transmission networks. The paper presents the study of mathematical modelling of electromagnetic wave processes in long-distance electric transmission line (ETL). The mathematical model is based on electromagnetic processes occurring on distributed parameter lines that are characterized by specific derivatives of the system of differential equations. The application of a spline-interpolation technique enables the calculation of currents and voltages at the nodes of the scheme, which obtains the unknown coordinates of the overhead line mode at the beginning of the ETL to solve the transmission line equation. The following results are derived from computer simulations of transients during switching on. With a simulation model, the importance of intelligent control of shunt reactor (SR) and ungrounded reactor (UR) was demonstrated and considered for a 500 kV power networks.

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Regularized Solution of the Cauchy Problem in an Unbounded Domain

Abstract: In this paper, using the construction of the Carleman matrix, we explicitly find a regularized solution of the Cauchy problem for matrix factorizations of the Helmholtz equation in a three-dimensional unbounded domain.

Cited by 5 publications

References 23 publications

Comparison of Approximate Analytical and Numerical Solutions of the Allen Cahn Equation

Comparison of Approximate Analytical and Numerical Solutions of the Allen Cahn Equation

Comparing the Performance of Two Butcher-Based Block Hybrid Algorithms for the Solution of Initial Value Problems

Calculation algorithm for electromagnetic wave processes in multi-wire intersystem ETL

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