Solution of Linear Volterra Integral Equation of Second Kind via Rishi Transform

Aggarwal, S.; Kumar, R.; Chandel, J.

doi:10.3329/jsr.v15i1.60337

Cited by 6 publications

(6 citation statements)

References 37 publications

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“…(C) Consider the following second type of Linear V.I.E. with a Faltung-type kernel (Aggarwal et al 2023):…”

Section: Numerical Applicationsmentioning

confidence: 99%

Utilizing the Upadhyaya Transform to solve the linear second kind Volterra Integral Equation

Thakur¹,

Thakur²

2023

RCSAS

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Volterra integral equations have a wide range of applications in mechanics, linear visco-elasticity, renewal theory, particle size statistics, damped vibration of a string, heat transfer problems, geometric probability, population dynamics, and epidemic studies. Many mathematicians and scientists are interested in finding either approximate or exact solutions to these equations. Upadhyaya Transform (UT) will be used in this paper to solve linear second type V.I.E. To accomplish this, the linear second type V.I.E. kernel has adopted a convolution type kernel. Some numerical examples are taken into account in order to outline the entire process of arriving at the solution. According to our findings, the Upadhyaya Transform (UT) is a powerful tool for finding solutions to the Linear Second kind V.I.E.

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“…(C) Consider the following second type of Linear V.I.E. with a Faltung-type kernel (Aggarwal et al 2023):…”

Section: Numerical Applicationsmentioning

confidence: 99%

Utilizing the Upadhyaya Transform to solve the linear second kind Volterra Integral Equation

Thakur¹,

Thakur²

2023

RCSAS

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“…et al [14] described Aboodh transform to solve some telegraph equations with specific initial conditions. Aggarwal S. et al [15] used recently developed transform method called Rishi transform to acquire the analytical solution of linear volterra integral equation. Also, Kuffi E. et al [16] introduced a new integral transform method named Emad-Falih transform to find the solutions of firstorder and second-order ordinary differential equations.…”

Section: Introductionmentioning

confidence: 99%

The New Integral Transform "Mohand Transform"

Özdoğan

2024

JISE

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Investigating solutions of differential equations has been an important issue for scientists. Researchers around the world have talked about different methods to solve differential equations. The type and order of the differential equation enabled us to decide the method that we could choose to find the solution of the equation. One of these methods is the integral transform. Integral transform is the conversion of a real or complex valued function into another function by some algebraic operations. Integral transforms are used to solve many problems in mathematics and engineering, such as differential equations and integral equations. Therefore, new types of integral transforms have been defined and existing integral transforms have been improved. One of the solution methods of many physical problems also initial and boundary value problems are integral transforms. Integral transforms were introduced in the first half of the 19th century. The first historically known integral transforms are Laplace and Fourier transforms. Over the time, other transforms have emerged that are used in many fields. In this article, mohand transform was described and used to simplify the solution of linear ordinary differential equations with constant coefficients.

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“…The system of linear Volterra integro-differential equations of the second kind (S-LVIDE-SK) is given by Aggarwal and Kumar (2021) { 𝐯 𝟏 (𝐦) Where the unknown functions 𝑣 1 (𝑡), 𝑣 2 (𝑡) … , 𝑣 𝑛 (𝑡) which will be determined, appear only inside the integral sign whilst the derivatives of v 1 (t), v 2 (t) … , v n (t) mostly occur outside the integral sign. The Kernels K ji (s, t), and the function h j (s) for j, i = 1, 2, … , n are given real-valued functions.…”

Section: Introductionmentioning

confidence: 99%

“…In recently years some researchers for solving system of Fredholm and Volterra integro-differential equations have used several techniques. Aggarwal and Kumar (2021) used Laplace-Carson transform for solving (S-LVIDE-SK). Jalal et al (2019) solved the (S-LVIDE-SK) by modified decomposition method.…”

Section: Introductionmentioning

confidence: 99%

SEE Transform Technique for Solving System of Linear Volterra Integro-Differential Equations of the Second Kind

Rustam

Sulaiman

2023

Polytechnic j.

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There are many integral transforms that are widely used to solve numerous real-life, science, and engineering problems. In this article, we present SEE transform for determining the solution of the system of linear Volterra integro-differential equations of the second kind. Some applications have been given and solved by using the SEE transform for illustrating the applicability of the SEE transform. Results of the applications assert that the SEE transform is very effective for obtaining the exact solution of this equation.

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Solution of Linear Volterra Integral Equation of Second Kind via Rishi Transform

Cited by 6 publications

References 37 publications

Utilizing the Upadhyaya Transform to solve the linear second kind Volterra Integral Equation

Utilizing the Upadhyaya Transform to solve the linear second kind Volterra Integral Equation

The New Integral Transform "Mohand Transform"

SEE Transform Technique for Solving System of Linear Volterra Integro-Differential Equations of the Second Kind

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