A novel approach to initial boundary value problems using Laplace transform Adomian decomposition method
*S. K. TalankarCorresponding authorsagartalankar7@gmail.comDepartment of MathematicsNanded Education Society’s Science CollegeNanded, Maharashtra, 431602, IndiaView full profile → , A. B. Jadhavarunbjadhao@gmail.comDepartment of MathematicsDnyanopasak CollegeParbhani, Maharashtra, 431401, IndiaView full profile → , R.A. MUNESHWARmuneshwarrajesh10@gmail.comDepartment of MathematicsNanded Education Society’s Science CollegeNanded, Maharashtra, 431602, IndiaView full profile →
* Corresponding author · click or hover a name for details
- Received:
- 10 Jan 2023
- Published Online:
- 30 Nov 2024
- Article type:
- Research Article
- Language:
- EN
- Article no.:
- JIM-2031
- Pages:
- 1701–1717
Abstract
Keywords
Subject Classifications
References
[1] J. Stoer and R. Bulirsch, Introduction to Numerical Analysis. Springer (2013).
[2] A. M. Wazwaz, Partial Differential Equations and Solitary Waves Theory. Higher Education Press, Beijing, and Springer-Verlag, Berlin Heidelberg (2009).
[3] L. Yong, ”Richardson iteration for linear equations and application in two-point boundary value problem,” Journal of Interdisciplinary Mathematics, vol. 21, no. 1, pp. 231-242 (2018), doi: 10.1080/09720502.2017.1303950.
[4] G. Wu and E. W. Lee, ”Fractional variational iteration method and its application,” Physics Letters A, vol. 374, pp. 2506-2509 (2010).
[5] A. M. Wazwaz, ”On the solution of the fourth-order parabolic equation by the decomposition method,” International Journal of Computer Mathematics, vol. 57, pp. 213-217 (1995).
[6] Y. Cherrualt and G. Adomian, ”Decomposition methods: A new proof of convergence,” Mathematics and Computers in Simulation, vol. 18, pp. 103-106 (1993).
[7] I. Podlubny, Fractional Differential Equations. Academic Press, USA (1999).
[8] W. R. Schneider and W. Wysaa, ”Fractional diffusion and wave equations,” Journal of Mathematical Physics, vol. 30, no. 1, pp. 134-144 (1989).
[9] V. Daftardar-Gejji and S. Bhalekar, ”Solving fractional boundary value problems with Dirichlet boundary conditions using a new iterative method,” Computers and Mathematics with Applications, vol. 59, no. 5, pp. 1801-1809, Mar. (2010).
[10] V. Daftardar-Gejji and H. Jafari, ”Boundary value problems for fractional diffusion-wave equations,” Australian Journal of Mathematical Analysis and Applications, vol. 3, pp. 1-8 (2006).
[11] J.-H. He, ”Approximate analytical solution for seepage flow with fractional derivative in porous media,” Computational Methods in Applied Mechanics and Engineering, vol. 167, pp. 57-68 (1998).
[12] M. A. Abdou and A. A. Soliman, ”New application of variational iteration method,” Physica D, vol. 211, pp. 1-8 (2005).
[13] I. Podlubny, ”The Laplace Transform Method for Linear Differential Equations of Fractional Order,” arXiv Preprint, funct-an/9710005, Oct. 30 (1997).
