A new transformation technique to find the analytical solution of general second order linear ordinary differential equation

Ahmed, Zulfiqar; Kalim, Muhammad; Economics, Lahore

doi:10.21833/ijaas.2018.04.014

Cited by 5 publications

(1 citation statement)

References 20 publications

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“…The proper choice of class of transformation usually makes it possible to convert not only the derivatives in an intractable differential equation but also the boundary values into terms of an algebraic equation that can be easily solved. The solution obtained is, of course, the transform of the solution of the original differential equation, and it is necessary to invert this transform to complete the operation [1,7,8,13].…”

Section: Introductionmentioning

confidence: 99%

On the convergence of double Sumudu transform

Ahmed¹,

Idrees²,

Belgacem³

et al. 2019

J. Nonlinear Sci. Appl.

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In this article, we have studied the convergence properties of double Sumudu transformation, and we presented the results in the form of theorems on convergence, absolute convergence, and uniform convergence of Double Sumudu transformation. The Double Sumudu transform of double Integral has also been discussed for integral evaluation. Finally, we have solved a Volterra integro-partial differential equation by using Double Sumudu transformation.

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Section: Introductionmentioning

confidence: 99%

On the convergence of double Sumudu transform

Ahmed¹,

Idrees²,

Belgacem³

et al. 2019

J. Nonlinear Sci. Appl.

Self Cite

View full text Add to dashboard Cite

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Solving Vertical Body Motion with Quadratic Resistance using Closed-form Solution for Ricatti Differential Equation of Constant Coefficients based on Discriminant Criteria

Rohedi

2021

J. Phys.: Conf. Ser.

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One of problem in mechanics is vertical body motion in upward and downward direction due to gravitational and resistance forces. In this paper, we are interested to analyse the effect of quadratic resistance force respect to the instantaneouly velocity and position of the body. The equation of the vertical body motion affected by gravitational and quadratic resistance forces derived using the second Newton law generally in the form of Riccati differential equation of constant coefficients. Therefore we need a method for solving the mathematics model. For the purpose we introduce a closed form solution for Riccati differential equation of constant coeficients based on discriminant criteria that can be used to solve the analytic model of vertical body motion by simple manner.

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Solving a Class of First-Order Nonlinear Ordinary Differential Equations Which Can Be Transformed into Confluent Hypergeometric Equation Based on Elastic Upgrading Transformation Method

付

2023

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A new transformation technique to find the analytical solution of general second order linear ordinary differential equation

Cited by 5 publications

References 20 publications

On the convergence of double Sumudu transform

On the convergence of double Sumudu transform

Solving Vertical Body Motion with Quadratic Resistance using Closed-form Solution for Ricatti Differential Equation of Constant Coefficients based on Discriminant Criteria

Solving a Class of First-Order Nonlinear Ordinary Differential Equations Which Can Be Transformed into Confluent Hypergeometric Equation Based on Elastic Upgrading Transformation Method

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