The Numerical And Approximate Analytical Solution Of Parabolic Partial Differential Equations With Nonlocal Boundary Conditions
| dc.contributor.author | Ghoreishi, Seyed Mohammad | |
| dc.date.accessioned | 2018-11-28T07:12:32Z | |
| dc.date.available | 2018-11-28T07:12:32Z | |
| dc.date.issued | 2011-12 | |
| dc.description.abstract | Many scientific and engineering problems can be modeled by parabolic partial dif- ferential equations with nonlocal boundary conditions. Examples of such problems can be found in chemical diffusion, thermoelasticity, heat conduction processes, nuclear reactor dynamics, inverse problems, control theory and so forth. In the last two decades, the development of numerical and approximate analytical tech- niques to solve these equations has been an important area of research due to the need to better understand the underlying physical phenomena. There is a need to develop new and more accurate techniques and this is the area of focus of this thesis. In this thesis, we propose new finite difference methods and study approxi- mate analytical methods for solving linear and nonhomogeneous parabolic partial differential equations with nonlocal boundary conditions. We have introduced a new explicit finite difference method and a new (3,3) Crandall- formula method and have discussed the obtained results. In addition, we have also studied sev- eral approximate analytical methods- Adomian Decomposition Method, Variation Iterative Method, Homotopy Perturbation Method, Homotopy Analysis Method, Optimal Homotopy Asymptotic Method and have applied the standard approach and modifications to solve linear and nonhomogeneous parabolic partial differential equations with nonlocal boundary conditions. It is known that the approximate analytical methods solve diferential equations by using the initial condition only. Thus, we also proposed a new modification of Adomian Decomposition Method to solve linear and nonhomogeneous parabolic partial differential equations with non- local boundary conditions by using nonlocal boundary conditions. We also show that the finite difference methods developed and approximate analytical methods considered are capable of accurately solving linear and nonhomogeneous parabolic partial differential equations with nonlocal boundary conditions. | en_US |
| dc.identifier.uri | http://hdl.handle.net/123456789/7147 | |
| dc.language.iso | en | en_US |
| dc.publisher | Universiti Sains Malaysia | en_US |
| dc.subject | The numerical and approximate analytical solution | en_US |
| dc.subject | of parabolic partial differential equations | en_US |
| dc.title | The Numerical And Approximate Analytical Solution Of Parabolic Partial Differential Equations With Nonlocal Boundary Conditions | en_US |
| dc.type | Thesis | en_US |
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