Analytical Solutions to Two-Dimensional Nonlinear Telegraph Equations Using the Conformable Triple Laplace Transform Iterative Method

Deresse, Alemayehu Tamirie

doi:10.1155/2022/4552179

Cited by 5 publications

(1 citation statement)

References 40 publications

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“…Numerous mathematicians and authors have created new methods to solve conformal differential problems, including the simplest method [26], Kudryashov method [27], double Shehu transform [28], Tanh method [29,30], reliable methods [31], double Sumudu transform [32,33], conformable Laplace transform (CLT) method [34,35], conformable double Laplace transform method [36], and conformable Sumudu transform (CST) method and others [37][38][39][40][41][42][43][44].…”

Section: Introductionmentioning

confidence: 99%

Modified conformable double Laplace–Sumudu approach with applications

Ahmed

Saadeh

Qazza

et al. 2023

Heliyon

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Section: Introductionmentioning

confidence: 99%

Modified conformable double Laplace–Sumudu approach with applications

Ahmed

Saadeh

Qazza

et al. 2023

Heliyon

View full text Add to dashboard Cite

Approximate Analytical Solution to Nonlinear Delay Differential Equations by Using Sumudu Iterative Method

Moltot

Deresse

2022

Advances in Mathematical Physics

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In this study, an efficient analytical method called the Sumudu Iterative Method (SIM) is introduced to obtain the solutions for the nonlinear delay differential equation (NDDE). This technique is a mixture of the Sumudu transform method and the new iterative method. The Sumudu transform method is used in this approach to solve the equation’s linear portion, and the new iterative method’s successive iterative producers are used to solve the equation’s nonlinear portion. Some basic properties and theorems which help us to solve the governing problem using the suggested approach are revised. The benefit of this approach is that it solves the equations directly and reliably, without the prerequisite for perturbations or linearization or extensive computer labor. Five sample instances from the DDEs are given to confirm the method’s reliability and effectiveness, and the outcomes are compared with the exact solution with the assistance of tables and graphs after taking the sum of the first eight iterations of the approximate solution. Furthermore, the findings indicate that the recommended strategy is encouraging for solving other types of nonlinear delay differential equations.

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Approximate Analytical Solution of Two-Dimensional Nonlinear Time-Fractional Damped Wave Equation in the Caputo Fractional Derivative Operator

Deresse

Mussa

Gizaw

2022

Mathematical Problems in Engineering

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In this work, we proposed a new method called Laplace–Padé–Caputo fractional reduced differential transform method (LPCFRDTM) for solving a two-dimensional nonlinear time-fractional damped wave equation subject to the appropriate initial conditions arising in various physical models. LPCFRDTM is the amalgamation of the Laplace transform method (LTM), Padé approximant, and the well-known reduced differential transform method (RDTM) in the Caputo fractional derivative senses. First, the solution to the problem is gained in the convergent power series form with the help of the Caputo fractional-reduced differential transform method. Then, the Laplace–Padé approximant is applied to enlarge the domain of convergence. The advantage of this method is that it solves equations simply and directly without requiring enormous amounts of computational work, perturbations, or linearization, and it expands the convergence domain, leading to the exact answer. To confirm the effectiveness, accuracy, and convergence of the proposed method, four test-modeling problems from mathematical physics nonlinear wave equations are considered. The findings and results showed that the proposed approach may be utilized to solve comparable wave equations with nonlinear damping and source components and to forecast and enrich the internal mechanism of nonlinearity in nonlinear dynamic events.

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Analytical Solutions to Two-Dimensional Nonlinear Telegraph Equations Using the Conformable Triple Laplace Transform Iterative Method

Cited by 5 publications

References 40 publications

Modified conformable double Laplace–Sumudu approach with applications

Modified conformable double Laplace–Sumudu approach with applications

Approximate Analytical Solution to Nonlinear Delay Differential Equations by Using Sumudu Iterative Method

Approximate Analytical Solution of Two-Dimensional Nonlinear Time-Fractional Damped Wave Equation in the Caputo Fractional Derivative Operator

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