Multi-peak solutions of non-linear elliptic singularly perturbed reaction-diffusion equations using finite element simulation
The present paper deals with a review of nonlinear reaction-diffusion models appearing in different branches of science and engineering. The multi-peak solutions of non-linear elliptic singularly perturbed reaction-diffusion equations do not appear to have been previously studied in detail, computat...
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| Published in | Journal of the Taiwan Institute of Chemical Engineers Vol. 50; pp. 56 - 68 |
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| Format | Journal Article |
| Language | English |
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01.05.2015
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| Abstract | The present paper deals with a review of nonlinear reaction-diffusion models appearing in different branches of science and engineering. The multi-peak solutions of non-linear elliptic singularly perturbed reaction-diffusion equations do not appear to have been previously studied in detail, computationally. The finite element method for the solution of non-linear elliptic singularly perturbed reaction-diffusion equations (subject to appropriate Dirichlet's boundary condition) is discussed, and a variant of Newton's method having fifth order of convergence is used to linearize the nonlinear system of equations. Examples of nonlinear elliptic singularly perturbed reaction-diffusion equation having non-linearity in homogeneous/non-homogeneous form are considered to show the existence of multi-peak solutions. |
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| AbstractList | The present paper deals with a review of nonlinear reaction-diffusion models appearing in different branches of science and engineering. The multi-peak solutions of non-linear elliptic singularly perturbed reaction-diffusion equations do not appear to have been previously studied in detail, computationally. The finite element method for the solution of non-linear elliptic singularly perturbed reaction-diffusion equations (subject to appropriate Dirichlet's boundary condition) is discussed, and a variant of Newton's method having fifth order of convergence is used to linearize the nonlinear system of equations. Examples of nonlinear elliptic singularly perturbed reaction-diffusion equation having non-linearity in homogeneous/non-homogeneous form are considered to show the existence of multi-peak solutions. |
| Author | Singh, Akhilesh Kumar Kumar, Manoj |
| Author_xml | – sequence: 1 givenname: Akhilesh Kumar surname: Singh fullname: Singh, Akhilesh Kumar email: au.akhilesh@gmail.com, akhilesh.singh@jiit.ac.in organization: Department of Mathematics, Jaypee Institute of Information Technology (Deemed University), Sector-128, Noida 201 304, U.P., India – sequence: 2 givenname: Manoj surname: Kumar fullname: Kumar, Manoj email: manoj@mnnit.ac.in organization: Department of Mathematics, Motilal Nehru National Institute of Technology, Allahabad 211 004, U.P |
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