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Efficient Approach for Solving (2+1) D- Differential Equations

Authors

  • Luma N. M. Tawfiq Department of Mathematics, College of Education for Pure Science Ibn Al-Haitham, University of Baghdad, Iraq https://orcid.org/0000-0001-5778-4983
  • Noor A. Hussein Department of Mathematics, College of Education, University of Al-Qadisiyah,Al-Diwaniyah , Iraq https://orcid.org/0000-0002-1279-2186

DOI:

https://doi.org/10.21123/bsj.2022.6541

Keywords:

Boussinesq equations, Cubic Klein-Gordon equations, Decomposition method, (2 1)-dimensional PDEs, Kadomtsev-Petviashvili equation

Abstract

     In this article, a new efficient approach is presented to solve a type of partial differential equations, such (2+1)-dimensional differential equations non-linear, and nonhomogeneous. The procedure of the new approach is suggested to solve important types of differential equations and get accurate analytic solutions i.e., exact solutions. The effectiveness of the suggested approach based on its properties compared with other approaches has been used to solve this type of differential equations such as the Adomain decomposition method, homotopy perturbation method, homotopy analysis method, and variation iteration method. The advantage of the present method has been illustrated by some examples.

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References

Salih H, Tawfiq LNM, Yahya ZRI, Zin SM. Solving Modified Regularized Long Wave Equation Using Collocation Method. J Phys Conf Ser. 2018, 1003(012062):1-10.

Tawfiq LNM, Hassan MA. Estimate the Effect of Rainwaters in Contaminated Soil by Using Simulink Technique. J Phys Conf Ser. 2018, 1003(012057): 1-7.

Tawfiq LNM, Jabber AK. Steady State Radial Flow in Anisotropic and Homogenous in Confined Aquifers. J Phys Conf Ser.2018, 1003(012056): 1-12.

Tawfiq LNM, Abood IN. Persons Camp Using Interpolation Method. J Phys Conf Ser. 2018, 1003 (012055): 1-10.

Tawfiq LNM, Al-Noor NH, Al-Noor TH. Estimate the Rate of Contamination in Baghdad Soils By Using Numerical Method. J Phys Conf Ser. 2019, 1294 (032020): 1-10.

Hussein NA, Tawfiq LNM. New Approach for Solving (2+1)-Dimensional Differential Equation. J Phys Conf Ser. 2021, 1818(012182): 1-13.

Salih H, Tawfiq LNM. Solution of Modified Equal Width Equation Using Quartic Trigonometric-Spline Method. J Phys Conf Ser. 2020, 1664 (012033): 1-10.

Enadi MO, Tawfiq LNM. New Approach for Solving Three Dimensional Space Partial Differential Equation. Baghdad Sci. J. 2019, 16(3): 786-792.

Ghazi, FF, Tawfiq, LNM. New Approach for Solving Two Dimensional Spaces PDE. J Phys Conf Ser. 2020.1530 (012066): 1-10.

Tawfiq LNM and Ali MH. Efficient Design of Neural Networks for Solving Third Order Partial Differential Equations. JPCS, 2020, 1530(012067): 1-8.

Tawfiq LNM, Salih OM. Design neural network based upon decomposition approach for solving reaction diffusion equation. J Phys Conf Ser. 2019, 1234 (012104): 1-8.

Tawfiq, L.N.M, Jasim K.A, Abdulhmeed, EO. Mathematical Model for Estimation the Concentration of Heavy Metals in Soil for Any Depth and Time and its Application in Iraq. International Journal of Advanced Scientific and Technical Research. 2015, 4(5): 718-726.

Hussein NA, Tawfiq LNM. New Approach for Solving (1+1)-Dimensional Differential Equation. J Phys Conf Ser. 2020, 1530(012098): 1-11.

Tawfiq LNM, Kareem ZH. Efficient Modification of the Decomposition Method for Solving a System of PDEs. Iraqi J Sci. 2021. 62( 9): 3061-3070.

Kareem ZH, Tawfiq LNM. Solving Three-Dimensional Groundwater Recharge Based on Decomposition Method. J Phys Conf Ser. 2020, 1530 (012068): 1-8.

Abdul-Majid Wazwaz. Partial Differential Equations and Solitary Waves Theory. Higher Education Press, Beijing and Springer. 2009. 353p. DOI:10.1007/978-3-642-00251-9

Tawfiq LNM, Ibrahim Abed AQ. Efficient Method for Solving Fourth Order PDEs. J Phys Conf Ser. 2021, 1818(012166): 1-10.

Tawfiq LNM, Altaie H. Recent Modification of Homotopy Perturbation Method for Solving System of Third Order PDEs.JPCS. 2020, 1530(012073): 1-8.

Tawfiq LNM, Oraibi YA. Fast Training Algorithms for Feed Forward Neural Networks. IHJPAS. 2017, 26(1): 275-280

.Mahmoud AE, Abdelrahman MA., Alharbi A. The new exact solutions for the deterministic and stochastic (2+1)-dimensional equations in natural sciences. J Taibah Univ Med Sci. 2019 Jul, 13(1): 834–843.

Wang Z, Zhang H-Q. Many new kinds exact solutions to (2+1)-dimensional Burgers equation and Klein-Gordon equation used a new method with symbolic computation. J Appl Math Comput. 2007, 186(1): 693–704.

Khan K, Akbar MA. Exact Solutions of the (2+1)-dimensional cubic Klein-Gordon Equation and the (3+1)- dimensional Zakharov-Kuznetsov equation using the modified simple equation method. J Assoc Arab Univ Basic Appl Sci. 2014, 15(1):74–81.

Enadi MO, Tawfiq, LNM. New Technique for Solving Autonomous Equations, IHJPAS, 2019, 32 (2): 123-130

Tawfiq LNM, Ali MH. Efficient Design of Neural Networks for Solving Third Order Partial Differential Equations. JPCS. 2020,1530(012067): 1-8.

Abazari R, Adem KJlJçman. Solitary Wave Solutions of the Boussinesq Equation and Its Improved Form. Math Probl Eng.2013, 2013:1-8.

Tawfiq LNM, Khamas AH. New Coupled Method for Solving Burger’s Equation. J Phys Conf Ser. 2020, 1530: 1-11.

Ajeel YJ, Kadhim SN. Some Common Fixed Points Theorems of Four Weakly Compatible Mappings in Metric Spaces. Baghdad Sci J. 2021, 18(3):543-546.

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