Abstract
References
- Zill D.G., A First Course in Differential Equations with Modeling Applications, 11th ed. Cengage Learning, 2017.
- Hairer E., Norsett S.P. and Wanner G., Solving Ordinary Differential Equations I: Nonstiff Problems, Berlin, New York: Springer-Verlag, 1993.
- Hand L.N. and Finch J.D., Analytical Mechanics, Cambridge, UK: Cambridge University Press, 1998.
- Fowles G.R. and Cassiday G.L., Analytical Mechanics, 7th ed. Brooks/Cole, 2004.
- Fasano A. and Marmi S., Analytical Mechanics, USA: Oxford University Press, 2006.
- Debnath L. and Bhatta D., Integral Transforms and Their Applications, 2nd ed. Boca Raton, FL: Chapman and Hall/CRC, 2007.
- Bracewell R.N., The Fourier Transform and Its Applications, 3rd ed. New York, USA: McGraw-Hill, 1986.
- Widder D.V., The Laplace Transform. Princeton, USA: Princeton University Press, 1946.
- Watugala G.K., ”Sumudu Transform: A New Integral Transform to Solve Differential Equations and Control Engineering Problems”, International Journal of Mathematical Education in Science and Technology, 24, (1993), 35-43.
- Al-Omari S.K.Q., ”On the Application of Natural Transforms”, International Journal of Pure and Applied Mathematics, 85(4), (2013), 729-744.
- Elzaki T.M., ”The New Integral Transform ’Elzaki Transform’”, Global Journal of Pure and Applied Mathematics, 7(1), (2011), 57-64.
- Maitama S., Zhao W., ”New Integral Transform: Shehu Transform a Generalization of Sumudu and Laplace Transform for Solving Differential Equations”, International Journal of Analysis and Applications, 17(2), (2019), 167- 190.
- Kashuri A., Fundo A., ”A New Integral Transform”, Advances in Theoretical and Applied Mathematics, 8(1), (2013), 27-43.
- Kashuri A., Fundo A., Liko R., ”On Double New Integral Transform and Double Laplace Transform”, European Scientific Journal, 9(33), (2013), 1857–7881.
- Shah K., Singh T., ”A Solution of the Burger’s Equation Arising in the Longitudinal Dispersion Phenomenon in Fluid Flow through Porous Media by Mixture of New Integral Transform and Homotopy Perturbation Method”, Journal of Geoscience and Environment Protection, 3, (2015), 24-30.
- Kashuri A., Fundo A., Liko R. ”New Integral Transform For Solving Some Fractional Differential Equations”, International Journal of Pure and Applied Mathematics, 103(4), (2015), 675-682.
- Shah K., Singh T., ”The Mixture of New Integral Transform and Homotopy Perturbation Method for Solving Discontinued Problems Arising in Nanotechnology”, Open Journal of Applied Sciences, 5, (2015), 688-695.
- Fundo A., Kashuri A., Liko R., ”New Integral Transform in Caputo Type Fractional Difference Operator”, Universal Journal of Applied Science, 4(1), (2016), 7-10.
- Güngör N., ”Solving Convolution Type Linear Volterra Integral Equations with Kashuri Fundo Transform”, Journal of Abstract and Computational Mathematics, 6(2), (2021), 1-7.
- Peker H.A., Cuha F.A., ”Application of Kashuri Fundo Transform and Homotopy Perturbation Methods to Fractional Heat Transfer and Porous Media Equations”, Thermal Science, 26(4A), (2022), 2877-2884.
- Cuha F.A., Peker H.A., ”Solution of Abel’s Integral Equation by Kashuri Fundo Transform”, Thermal Science, 26(4A), (2022), 3003-3010.
- Peker H. A., Cuha F. A., Peker B., ”Solving Steady Heat Transfer Problems via Kashuri Fundo Transform”, Thermal Science, 26(4A), (2022), 3011-3017.
- Subartini B., Sumiati I., Sukono, Riaman, Sulaiman I.M., ”Combined Adomian Decomposition Method with Integral Transform”, Mathematics and Statistics, 9(6), (2021) 976-983.
Abstract
Differential equations are expressions that are frequently encountered in mathematical modeling of laws or problems in many different fields of science. It can find its place in many fields such as applied mathematics, physics, chemistry, finance, economics, engineering, etc. They make them more understandable and easier to interpret, by modeling laws or problems mathematically. Therefore, solutions of differential equations are very important. Many methods have been developed that can be used to reach solutions of differential equations. One of these methods is integral transforms. Studies have shown that the use of integral transforms in the solutions of differential equations is a very effective method to reach solutions. In this study, we are looking for a solution to damped and undamped simple harmonic oscillations modeled by linear ordinary differential equations by using Kashuri Fundo transform, which is one of the integral transforms. From the solutions, it can be concluded that the Kashuri Fundo transform is an effective method for reaching the solutions of ordinary differential equations.
Keywords
Kashuri Fundo transform inverse Kashuri Fundo transform undamped simple harmonic oscillation damped simple harmonic oscillation differential equation
References
- Zill D.G., A First Course in Differential Equations with Modeling Applications, 11th ed. Cengage Learning, 2017.
- Hairer E., Norsett S.P. and Wanner G., Solving Ordinary Differential Equations I: Nonstiff Problems, Berlin, New York: Springer-Verlag, 1993.
- Hand L.N. and Finch J.D., Analytical Mechanics, Cambridge, UK: Cambridge University Press, 1998.
- Fowles G.R. and Cassiday G.L., Analytical Mechanics, 7th ed. Brooks/Cole, 2004.
- Fasano A. and Marmi S., Analytical Mechanics, USA: Oxford University Press, 2006.
- Debnath L. and Bhatta D., Integral Transforms and Their Applications, 2nd ed. Boca Raton, FL: Chapman and Hall/CRC, 2007.
- Bracewell R.N., The Fourier Transform and Its Applications, 3rd ed. New York, USA: McGraw-Hill, 1986.
- Widder D.V., The Laplace Transform. Princeton, USA: Princeton University Press, 1946.
- Watugala G.K., ”Sumudu Transform: A New Integral Transform to Solve Differential Equations and Control Engineering Problems”, International Journal of Mathematical Education in Science and Technology, 24, (1993), 35-43.
- Al-Omari S.K.Q., ”On the Application of Natural Transforms”, International Journal of Pure and Applied Mathematics, 85(4), (2013), 729-744.
- Elzaki T.M., ”The New Integral Transform ’Elzaki Transform’”, Global Journal of Pure and Applied Mathematics, 7(1), (2011), 57-64.
- Maitama S., Zhao W., ”New Integral Transform: Shehu Transform a Generalization of Sumudu and Laplace Transform for Solving Differential Equations”, International Journal of Analysis and Applications, 17(2), (2019), 167- 190.
- Kashuri A., Fundo A., ”A New Integral Transform”, Advances in Theoretical and Applied Mathematics, 8(1), (2013), 27-43.
- Kashuri A., Fundo A., Liko R., ”On Double New Integral Transform and Double Laplace Transform”, European Scientific Journal, 9(33), (2013), 1857–7881.
- Shah K., Singh T., ”A Solution of the Burger’s Equation Arising in the Longitudinal Dispersion Phenomenon in Fluid Flow through Porous Media by Mixture of New Integral Transform and Homotopy Perturbation Method”, Journal of Geoscience and Environment Protection, 3, (2015), 24-30.
- Kashuri A., Fundo A., Liko R. ”New Integral Transform For Solving Some Fractional Differential Equations”, International Journal of Pure and Applied Mathematics, 103(4), (2015), 675-682.
- Shah K., Singh T., ”The Mixture of New Integral Transform and Homotopy Perturbation Method for Solving Discontinued Problems Arising in Nanotechnology”, Open Journal of Applied Sciences, 5, (2015), 688-695.
- Fundo A., Kashuri A., Liko R., ”New Integral Transform in Caputo Type Fractional Difference Operator”, Universal Journal of Applied Science, 4(1), (2016), 7-10.
- Güngör N., ”Solving Convolution Type Linear Volterra Integral Equations with Kashuri Fundo Transform”, Journal of Abstract and Computational Mathematics, 6(2), (2021), 1-7.
- Peker H.A., Cuha F.A., ”Application of Kashuri Fundo Transform and Homotopy Perturbation Methods to Fractional Heat Transfer and Porous Media Equations”, Thermal Science, 26(4A), (2022), 2877-2884.
- Cuha F.A., Peker H.A., ”Solution of Abel’s Integral Equation by Kashuri Fundo Transform”, Thermal Science, 26(4A), (2022), 3003-3010.
- Peker H. A., Cuha F. A., Peker B., ”Solving Steady Heat Transfer Problems via Kashuri Fundo Transform”, Thermal Science, 26(4A), (2022), 3011-3017.
- Subartini B., Sumiati I., Sukono, Riaman, Sulaiman I.M., ”Combined Adomian Decomposition Method with Integral Transform”, Mathematics and Statistics, 9(6), (2021) 976-983.
Details
| Primary Language | English |
|---|---|
| Subjects | Engineering |
| Journal Section | Research Article |
| Authors | |
| Early Pub Date | June 23, 2023 |
| Publication Date | July 1, 2023 |
| Published in Issue | Year 2023 Volume: 11 Issue: 1 |
Cite
Manas Journal of Engineering