Solving Partial Integro-Differential Equations Using Laplace Transform Method

Thorwe, Jyoti

doi:10.5923/j.ajcam.20120203.06

Cited by 18 publications

(9 citation statements)

References 14 publications

(14 reference statements)

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“…Examples of numerical methods are: iterative, Newton-Raphson division, Newton's, Horner's, rate of convergence, Taylor series, Runge-Kutta, Laplace transform, Elzaki transform, double Elzaki transform linear, multistep, and Gear. They are used to solve realtime (i.e., dynamic) systems with assumptions made of the initial conditions [8], [10], [11].…”

Section: Basic Concepts a Numerical Methodsmentioning

confidence: 99%

Solving Partial Integro-Differential Equations with Weakly Singular Kernel

Hussain¹

2020

Journal of Southwest Jiaotong University

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Equations with a combination of integrals and derivatives are known as integro-differential equations. They are a combination of science and engineering. Many models are implemented with the help of integro-differential equations. Various techniques are available to solve integro-differential equations. In the present study, the Radial Basis Function and Adomain Decomposition Method-based numerical algorithms are used to solve a linear partial integro-differential equation with weakly singular kernel, which arises from viscoelasticity. In the discretization process, singular integrals were compared with the product trapezoidal method. Implementation of various radial basis functions was carried out. The proposed system was found to be useful and to provide reproducible results.

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Section: Basic Concepts a Numerical Methodsmentioning

confidence: 99%

Solving Partial Integro-Differential Equations with Weakly Singular Kernel

Hussain¹

2020

Journal of Southwest Jiaotong University

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“…The analysis of such PIDE can be found in [5][6][7][8]. In the last few years, Jyoti Thorwe and Sachin Bhalekar [1] Where, a i , b i , c and d i are constants or the functions of x alone. And f(x, t) , K i (t − y) are known functions.…”

Section: Introductionmentioning

confidence: 99%

Solving Partial Integro Differential Equations using Modified Differential Transform Method

Pardeshi¹,

Kulakarni²

2020

AJAST

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Solving this ODE and applying inverse transform they obtain the exact solution of the problem. Ranjit Dhunde and G. L. Waghmare [2] used double Laplace transform and Mohand M. Abdelrahim Mehgob [4] applied double Elzaki transform to solve PIDE. They converted PIDE to an algebraic equation and Appling inverse transform they obtained exact solution. Differential Transform Method is a semi-analytical numerical technique which depends on Taylor's series for the solution of differential and integral equations. The concept of differential transform method was first introduced by Zhou [9] who solved linear and non-linear initial value problems in electric circuit analysis. Recently, The various types of differential equations, integro differential equations, and Volterra integral equations solved by using two-dimensional DTM [12-19]. The modified differential transform method is a modified version of two-dimensional DTM, and it will take less computational time and effort to solve PIDEs. In this paper, we will find an analytical-numerical solution of linear partial integro differential equations (PIDE) with convolution kernel using a modified differential transform method.

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“…In [28] the solution of classical PIDEs was discussed using classical Laplace transform. In the present article we investigate the solution of different types of fuzzy partial integro differential equations with convolution kernel (FPIDEs) using fuzzy Laplace transform method.…”

Section: Introductionmentioning

confidence: 99%

Application of fuzzy Laplace transforms for solving fuzzy partial Volterra integro-differential equations

Ullah¹,

Farooq²,

Ahmad³

et al. 2014

Preprint

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Fuzzy partial integro-differential equations have a major role in the fields of science and engineering. In this paper, we propose the solution of fuzzy partial Volterra integro-differential equation with convolution type kernel using fuzzy Laplace transform method (FLTM) under Hukuhara differentiability. It is shown that FLTM is a simple and reliable approach for solving such equations analytically. Finally, the method is illustrated with few examples to show the ability of the proposed method.

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Solving Partial Integro-Differential Equations Using Laplace Transform Method

Cited by 18 publications

References 14 publications

Solving Partial Integro-Differential Equations with Weakly Singular Kernel

Solving Partial Integro-Differential Equations with Weakly Singular Kernel

Solving Partial Integro Differential Equations using Modified Differential Transform Method

Application of fuzzy Laplace transforms for solving fuzzy partial Volterra integro-differential equations

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