Variational Iteration Method
The variational iteration method (VIM) is one of the well‐known semi‐analytical methods for solving linear and nonlinear ordinary as well as partial differential equations. The main advantage of the method lies in its flexibility and ability to solve nonlinear equations easily....
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| Vydané v: | Advanced Numerical and Semi-Analytical Methods for Differential Equations s. 141 - 147 |
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| Hlavní autori: | , , , |
| Médium: | Kapitola |
| Jazyk: | English |
| Vydavateľské údaje: |
United States
Wiley
2019
John Wiley & Sons, Incorporated John Wiley & Sons, Inc |
| Vydanie: | 1 |
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| ISBN: | 9781119423423, 1119423422 |
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| Abstract | The variational iteration method (VIM) is one of the well‐known semi‐analytical methods for solving linear and nonlinear ordinary as well as partial differential equations. The main advantage of the method lies in its flexibility and ability to solve nonlinear equations easily. The method can be used in bounded and unbounded domains as well. By this method one can find the convergent successive approximations of the exact solution of the differential equations if such a solution exists. Wazwaz used the VIM for solving the linear and nonlinear Volterra integral and integro‐differential equations and explained clearly how to use this method for solving homogenous and inhomogeneous partial differential equations. This chapter solves few test problems using the present method to make the readers familiar with the method. As such, two linear nonhomogeneous partial differential equations are handled in two examples, and a nonlinear partial differential equation has been solved in other example. |
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| AbstractList | The variational iteration method (VIM) is one of the well‐known semi‐analytical methods for solving linear and nonlinear ordinary as well as partial differential equations. The main advantage of the method lies in its flexibility and ability to solve nonlinear equations easily. The method can be used in bounded and unbounded domains as well. By this method one can find the convergent successive approximations of the exact solution of the differential equations if such a solution exists. Wazwaz used the VIM for solving the linear and nonlinear Volterra integral and integro‐differential equations and explained clearly how to use this method for solving homogenous and inhomogeneous partial differential equations. This chapter solves few test problems using the present method to make the readers familiar with the method. As such, two linear nonhomogeneous partial differential equations are handled in two examples, and a nonlinear partial differential equation has been solved in other example. The variational iteration method (VIM) is one of the well‐known semi‐analytical methods for solving linear and nonlinear ordinary as well as partial differential equations. The main advantage of the method lies in its flexibility and ability to solve nonlinear equations easily. The method can be used in bounded and unbounded domains as well. By this method one can find the convergent successive approximations of the exact solution of the differential equations if such a solution exists. Wazwaz used the VIM for solving the linear and nonlinear Volterra integral and integro‐differential equations and explained clearly how to use this method for solving homogenous and inhomogeneous partial differential equations. This chapter solves few test problems using the present method to make the readers familiar with the method. As such, two linear nonhomogeneous partial differential equations are handled in two examples, and a nonlinear partial differential equation has been solved in other example. |
| Author | Karunakar, Perumandla Dilleswar Rao, Tharasi Mahato, Nisha Chakraverty, Snehashish |
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| Keywords | Nonhomogeneous media Nonlinear equations Integral equations Nonlinear systems |
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| References | He (c13-cit-0001) 1998; 167 Wazwaz (c13-cit-0003) 2010; 87 Wazwaz (c13-cit-0004) 2010 He (c13-cit-0005) 2000; 114 He, Wu (c13-cit-0002) 2007; 54 |
| References_xml | – volume: 54 start-page: 881 issue: 7/8 year: 2007 end-page: 894 ident: c13-cit-0002 article-title: Variational iteration method: new development and applications publication-title: Computers and Mathematics with Applications – volume: 87 start-page: 1131 issue: 5 year: 2010 end-page: 1141 ident: c13-cit-0003 article-title: The variational iteration method for solving linear and nonlinear Volterra integral and integro‐differential equations publication-title: International Journal of Computer Mathematics – volume: 167 start-page: 57 issue: 1–2 year: 1998 end-page: 68 ident: c13-cit-0001 article-title: Approximate analytical solution for seepage flow with fractional derivatives in porous media publication-title: Computer Methods in Applied Mechanics and Engineering – volume: 114 start-page: 115 issue: 2 year: 2000 end-page: 123 ident: c13-cit-0005 article-title: Variational iteration method for autonomous ordinary differential systems publication-title: Applied Mathematics and Computation – year: 2010 ident: c13-cit-0004 article-title: Partial Differential Equations and Solitary Waves Theory |
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| Snippet | The variational iteration method (VIM) is one of the well‐known semi‐analytical methods for solving linear and nonlinear ordinary as well as... The variational iteration method (VIM) is one of the well‐known semi‐analytical methods for solving linear and nonlinear ordinary as well as partial... |
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| SubjectTerms | linear nonhomogeneous partial differential equations nonlinear nonhomogeneous partial differential equation semi‐analytical methods variational iteration method |
| Title | Variational Iteration Method |
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