This research paper deals with the boundary and initial value problems for the Bratu-type model by using the New Improved Variational Homotopy Perturbation Method. The New Method does not require discritization, linea...This research paper deals with the boundary and initial value problems for the Bratu-type model by using the New Improved Variational Homotopy Perturbation Method. The New Method does not require discritization, linearization or any restrictive assumption of any form in providing analytical or approximate solutions to linear and nonlinear equation without the integral related with nonlinear term. Theses virtues make it to be reliable and its efficiency is demonstrated with numerical examples.展开更多
In this paper, we apply Exp-function method to give traveling wave solutions of second order sine-Bratu type equations. This method is straightforward, concise and effective.
We present the optimal homotopy asymptotic method (OHAM) to find the numerical solution of the second order initial value problems of Bratu-type. We solve some examples to illustrate the validity and efficiency of the...We present the optimal homotopy asymptotic method (OHAM) to find the numerical solution of the second order initial value problems of Bratu-type. We solve some examples to illustrate the validity and efficiency of the method.展开更多
The purpose of this paper is to employ the Adomian Decomposition Method (ADM) and Restarted Adomian Decomposition Method (RADM) with new useful techniques to resolve Bratu’s boundary value problem by using a new inte...The purpose of this paper is to employ the Adomian Decomposition Method (ADM) and Restarted Adomian Decomposition Method (RADM) with new useful techniques to resolve Bratu’s boundary value problem by using a new integral operator. The solutions obtained in this way require the use of the boundary conditions directly. The obtained results indicate that the new techniques give more suitable and accurate solutions for the Bratu-type problem, compared with those for the ADM and its modification.展开更多
This article is concerned with the numerical detection of bifurcation points of nonlinear partial differential equations as some parameter of interest is varied.In particular,we study in detail the numerical approxima...This article is concerned with the numerical detection of bifurcation points of nonlinear partial differential equations as some parameter of interest is varied.In particular,we study in detail the numerical approximation of the Bratu problem,based on exploiting the symmetric version of the interior penalty discontinuous Galerkin finite element method.A framework for a posteriori control of the discretization error in the computed critical parameter value is developed based upon the application of the dual weighted residual(DWR)approach.Numerical experiments are presented to highlight the practical performance of the proposed a posteriori error estimator.展开更多
Several problems arising in science and engineering are modeled by differential equations that involve conditions that are specified at more than one point. The non-linear two-point boundary value problem (TPBVP) (Br...Several problems arising in science and engineering are modeled by differential equations that involve conditions that are specified at more than one point. The non-linear two-point boundary value problem (TPBVP) (Bratu’s equation, Troesch’s problems) occurs engineering and science, including the modeling of chemical reactions diffusion processes and heat transfer. An analytical expression pertaining to the concentration of substrate is obtained using Homotopy perturbation method for all values of parameters. These approximate analytical results were found to be in good agreement with the simulation results.展开更多
文摘This research paper deals with the boundary and initial value problems for the Bratu-type model by using the New Improved Variational Homotopy Perturbation Method. The New Method does not require discritization, linearization or any restrictive assumption of any form in providing analytical or approximate solutions to linear and nonlinear equation without the integral related with nonlinear term. Theses virtues make it to be reliable and its efficiency is demonstrated with numerical examples.
文摘In this paper, we apply Exp-function method to give traveling wave solutions of second order sine-Bratu type equations. This method is straightforward, concise and effective.
文摘We present the optimal homotopy asymptotic method (OHAM) to find the numerical solution of the second order initial value problems of Bratu-type. We solve some examples to illustrate the validity and efficiency of the method.
文摘The purpose of this paper is to employ the Adomian Decomposition Method (ADM) and Restarted Adomian Decomposition Method (RADM) with new useful techniques to resolve Bratu’s boundary value problem by using a new integral operator. The solutions obtained in this way require the use of the boundary conditions directly. The obtained results indicate that the new techniques give more suitable and accurate solutions for the Bratu-type problem, compared with those for the ADM and its modification.
基金the financial support of the EPSRC under the grant EP/E013724the support of the EPSRC under the grant EP/F01340X.
文摘This article is concerned with the numerical detection of bifurcation points of nonlinear partial differential equations as some parameter of interest is varied.In particular,we study in detail the numerical approximation of the Bratu problem,based on exploiting the symmetric version of the interior penalty discontinuous Galerkin finite element method.A framework for a posteriori control of the discretization error in the computed critical parameter value is developed based upon the application of the dual weighted residual(DWR)approach.Numerical experiments are presented to highlight the practical performance of the proposed a posteriori error estimator.
文摘Several problems arising in science and engineering are modeled by differential equations that involve conditions that are specified at more than one point. The non-linear two-point boundary value problem (TPBVP) (Bratu’s equation, Troesch’s problems) occurs engineering and science, including the modeling of chemical reactions diffusion processes and heat transfer. An analytical expression pertaining to the concentration of substrate is obtained using Homotopy perturbation method for all values of parameters. These approximate analytical results were found to be in good agreement with the simulation results.
