# Applications of Laplace Decomposition Method and Variational Iteration Transform Method to Solve Laplace Equation

### Abstract

In this paper, we implement Laplace decomposition method (LDM) and variational iteration transform method (VITM),which are analytical numerical techniques to Laplace equation. The methods provide the solution in the form of a rapidlyconvergent series. The methods are illustrated by two examples of Laplace equation and solutions are obtained. Theresults reveal that the proposed methods are very effective and simple.### References

[1] N. Asmar, "Partial Differential Equations", Prentice Hall, New Jersey, (2005).

[2] L.C. Evans, "Partial Differential Equations", AMS, Providence, (1998).

[3] M.S. Gockenbach, "Partial Differential Equations", SIAM, Philadelphia, (2002).

[4] R. Haberman, "Applied Partial Differential Equations", Pearson, New York, (2003).

[5] A.P. Selvaduri, "Partial Differential Equations in Mechanics", Springer, Berlin (2000).

[6] A.M. Wazwaz, Partial Differential Equations: Methods and Applications, Bal-kema Publishers, The Netherlands,

(2002).

[7] G.B. Whitham, Linear and Nonlinear Waves , John Wiley, New York, (1976).

[8] A. M. Wazwaz, The variational iteration method for exact solutions of Laplace equation, Phys. Lett. A 363(2007) 260-

262.

[9] H. K. Jassim, Homotopy Perturbation Algorithm Using Laplace Transform for Newell-Whitehead-Segel Equation,

International Journal of Advances in Applied Mathematics and Mechanics, 2 (2015) 8-12.

[10] S. Abbasbandy., M.T. Darvishi, A numerical solution of Burger’s equation by time discrimination of Adomian's

decomposition method, Appl. math. Comput 170(2005) 95-102.

[11] M. Inc, On exact solution of Laplace equation with Dirichlet and Neumann boundary conditions by the homotopy

analysis method, Phys. Lett. A 365(2007) 412-415.

[12] D-H Shou, J-H He, Beyond Adomain method: The variational iteration method for solving heat-like and wave-like

equations with variable coefficients, Phys. Lett. A, 372(2008) 233-237.

[13] Khuri, S.A., A Laplace decomposition algorithm applied to class of nonlinear differential equations. J. Math, Appl.,

4(2001)141-155.

[14] Khuri, S.A., A new approach to Bratu’s problem. J. Math, Appl., 147(2004)131-136.

[2] L.C. Evans, "Partial Differential Equations", AMS, Providence, (1998).

[3] M.S. Gockenbach, "Partial Differential Equations", SIAM, Philadelphia, (2002).

[4] R. Haberman, "Applied Partial Differential Equations", Pearson, New York, (2003).

[5] A.P. Selvaduri, "Partial Differential Equations in Mechanics", Springer, Berlin (2000).

[6] A.M. Wazwaz, Partial Differential Equations: Methods and Applications, Bal-kema Publishers, The Netherlands,

(2002).

[7] G.B. Whitham, Linear and Nonlinear Waves , John Wiley, New York, (1976).

[8] A. M. Wazwaz, The variational iteration method for exact solutions of Laplace equation, Phys. Lett. A 363(2007) 260-

262.

[9] H. K. Jassim, Homotopy Perturbation Algorithm Using Laplace Transform for Newell-Whitehead-Segel Equation,

International Journal of Advances in Applied Mathematics and Mechanics, 2 (2015) 8-12.

[10] S. Abbasbandy., M.T. Darvishi, A numerical solution of Burger’s equation by time discrimination of Adomian's

decomposition method, Appl. math. Comput 170(2005) 95-102.

[11] M. Inc, On exact solution of Laplace equation with Dirichlet and Neumann boundary conditions by the homotopy

analysis method, Phys. Lett. A 365(2007) 412-415.

[12] D-H Shou, J-H He, Beyond Adomain method: The variational iteration method for solving heat-like and wave-like

equations with variable coefficients, Phys. Lett. A, 372(2008) 233-237.

[13] Khuri, S.A., A Laplace decomposition algorithm applied to class of nonlinear differential equations. J. Math, Appl.,

4(2001)141-155.

[14] Khuri, S.A., A new approach to Bratu’s problem. J. Math, Appl., 147(2004)131-136.

Published

2018-03-13

How to Cite

JASSIM, Hassan Kamil.
Applications of Laplace Decomposition Method and Variational Iteration Transform Method to Solve Laplace Equation.

**Universal Journal of Mathematics**, [S.l.], v. 1, n. 1, p. 1-8, mar. 2018. ISSN 2456-1312. Available at: <http://uproonline.com/index.php/UJM/article/view/10>. Date accessed: 22 sep. 2018.
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Section

Articles

### Keywords

Laplace equation; Laplace decomposition method; Variational iteration transform method; Laplace transform