Research Article
Year 2023,
Volume: 44 Issue: 1, 160 - 169, 26.03.2023
Abstract
Supporting Institution
yok
Project Number
yok
References
- [1] Khuri S.A., A new approach to Bratu’s problem, Appl. Math. Comput., 147 (2004) 131– 136.
- [2] Kiymaz O., An algorithm for solving initial value problems using Laplace Adomian Decomposition Method, Appl. Math. Sci., 3 (30) (2009) 1453–1459.
- [3] Babolian E., Biazar J., Vahidi A.R., A new computational method for Laplace transforms by decomposition method, Appl. Math. Comput., 150 (2004) 841–846
- [4] Merdan M., Homotopy perturbation Method for solving a model for infection of CD4 +T cells, İstanbul Ticaret Üniversitesi Fen Bilimleri Dergisi.,12 (2007) 39–52.
- [5] Yusufoglu E., Numerical solution of Duffing equation by the Laplace decomposition algorithm, Appl. Math. Comput., 177 (2) (2006) 572–580.
- [6] Abbasbandy S., Application of He’s homotopy perturbation method for Laplace transform, Chaos Solitons Fractals., 30 (2006) 1206–1212.
- [7] Khuri S.A., A Laplace decomposition algorithm applied to a class of nonlinear differential equations, J. Appl. Math., 1 (4) (2001) 141–155.
- [8] Jafari H, Khalique C.M., Nazari M., Application of the Laplace decomposition method for solving linear and nonlinear fractional diffusion–wave equations, Appl. Math. Lett., 24 (2011) 1799–1805.
- [9] Mohamed M.Z., Comparison between the Laplace Decomposition Method and Adomian Decomposition in Time-Space Fractional Nonlinear Fractional Differential Equations, Appl. Math., 9 (2018) 448.
- [10] Gaxiola O.G., The Laplace-Adomian decomposition method applied to the Kundu–Eckhaus equation, Int. J. Math. Its Appl.,5 (2017) 1–12.
- [11] Al-Zurigat, M., Solving nonlinear fractional differential equation using a multi-step Laplace Adomian decomposition method, Ann. Univ. Craiova-Math. Comput. Sci. Ser.,39 (2012) 200–210.
- [12] Haq F., Shah K., Rahman ur G., Shahzad M., Numerical solution of fractional order smoking model via laplace Adomian decomposition method, Alex. Eng. J., 57 (2018) 1061–1069.
- [13] Morales-Delgado V.F., Taneco-Hernández M.A., Gómez-Aguilar J.F., On the solutions of fractional order of evolution equations, Eur. Phys. J. Plus.,132 (2017) 47.
- [14] Bekiryazici Z., Merdan M., Kesemen T., Modification of the random differential transformation method and its applications to compartmental models, Communications in Statistics-Theory and Methods., 50(18) (2021) 4271-4292.
- [15] Liao, S. J., On the proposed homotopy analysis technique for nonlinear problems and its applications. Shanghai Jiao Tong University, (1992).
- [16] Liao S.J., An approximate solution technique which does not depend upon small parameters: a special example. Int J Nonlinear Mech, (1995) 30:371–80.
- [17] Liao S.J., An approximate solution technique which does not depend upon small parameters (II): an application in fluid mechanics. Int J Nonlinear Mech, (1997) 32:815–22.
Year 2023,
Volume: 44 Issue: 1, 160 - 169, 26.03.2023
Abstract
In this study, random partial differential equations obtained by randomly choosing the coefficients or initial conditions of partial differential equations will be analyzed. With the help of Laplace Adomian Decomposition Method and Homotopy Analysis Method, approximate analytical solutions of random partial differential equations were obtained. Initial conditions and parameters are made into random variables with normal distribution and gamma distribution. Probability characteristics such as expected value, variance and confidence intervals of the obtained random partial differential equation are calculated. Obtained results will be plotted with the help of MATLAB (2013a), package program and random results will be interpreted.
Keywords
Random partial differential equation Normal distribution Laplace-Adomian decomposition method Gamma distribution.
Project Number
yok
References
- [1] Khuri S.A., A new approach to Bratu’s problem, Appl. Math. Comput., 147 (2004) 131– 136.
- [2] Kiymaz O., An algorithm for solving initial value problems using Laplace Adomian Decomposition Method, Appl. Math. Sci., 3 (30) (2009) 1453–1459.
- [3] Babolian E., Biazar J., Vahidi A.R., A new computational method for Laplace transforms by decomposition method, Appl. Math. Comput., 150 (2004) 841–846
- [4] Merdan M., Homotopy perturbation Method for solving a model for infection of CD4 +T cells, İstanbul Ticaret Üniversitesi Fen Bilimleri Dergisi.,12 (2007) 39–52.
- [5] Yusufoglu E., Numerical solution of Duffing equation by the Laplace decomposition algorithm, Appl. Math. Comput., 177 (2) (2006) 572–580.
- [6] Abbasbandy S., Application of He’s homotopy perturbation method for Laplace transform, Chaos Solitons Fractals., 30 (2006) 1206–1212.
- [7] Khuri S.A., A Laplace decomposition algorithm applied to a class of nonlinear differential equations, J. Appl. Math., 1 (4) (2001) 141–155.
- [8] Jafari H, Khalique C.M., Nazari M., Application of the Laplace decomposition method for solving linear and nonlinear fractional diffusion–wave equations, Appl. Math. Lett., 24 (2011) 1799–1805.
- [9] Mohamed M.Z., Comparison between the Laplace Decomposition Method and Adomian Decomposition in Time-Space Fractional Nonlinear Fractional Differential Equations, Appl. Math., 9 (2018) 448.
- [10] Gaxiola O.G., The Laplace-Adomian decomposition method applied to the Kundu–Eckhaus equation, Int. J. Math. Its Appl.,5 (2017) 1–12.
- [11] Al-Zurigat, M., Solving nonlinear fractional differential equation using a multi-step Laplace Adomian decomposition method, Ann. Univ. Craiova-Math. Comput. Sci. Ser.,39 (2012) 200–210.
- [12] Haq F., Shah K., Rahman ur G., Shahzad M., Numerical solution of fractional order smoking model via laplace Adomian decomposition method, Alex. Eng. J., 57 (2018) 1061–1069.
- [13] Morales-Delgado V.F., Taneco-Hernández M.A., Gómez-Aguilar J.F., On the solutions of fractional order of evolution equations, Eur. Phys. J. Plus.,132 (2017) 47.
- [14] Bekiryazici Z., Merdan M., Kesemen T., Modification of the random differential transformation method and its applications to compartmental models, Communications in Statistics-Theory and Methods., 50(18) (2021) 4271-4292.
- [15] Liao, S. J., On the proposed homotopy analysis technique for nonlinear problems and its applications. Shanghai Jiao Tong University, (1992).
- [16] Liao S.J., An approximate solution technique which does not depend upon small parameters: a special example. Int J Nonlinear Mech, (1995) 30:371–80.
- [17] Liao S.J., An approximate solution technique which does not depend upon small parameters (II): an application in fluid mechanics. Int J Nonlinear Mech, (1997) 32:815–22.
There are 17 citations in total.
Details
| Primary Language | English |
|---|---|
| Subjects | Mathematical Sciences |
| Journal Section | Natural Sciences |
| Authors | |
| Project Number | yok |
| Publication Date | March 26, 2023 |
| Submission Date | May 23, 2022 |
| Acceptance Date | February 5, 2023 |
| Published in Issue | Year 2023Volume: 44 Issue: 1 |
