Abstract
Singular nonlinear initial-value problems (IVPs) in first-order and second-order partial differential equations (PDEs) arising in fluid mechanics are semianalytically solved. To achieve this, the modified decomposition method (MDM) is used in conjunction with some new inverse differential operators. In other words, new inverse differential operators are developed for the MDM and used with the MDM to solve first- and second-order singular nonlinear PDEs. The results of the solutions by the MDM together with new inverse operators are compared with the existing exact analytical solutions. The comparisons show excellent agreement.
Highlights
Singular nonlinear partial differential equations (PDEs) arise in various physical phenomena in applied sciences and engineering from such areas as fluid mechanics and heat transfer, Riemannian geometry, applied probability, mathematical physics, and biology
modified decomposition method (MDM) was first developed by Wazwaz and El-Seyed [1] who applied it to solve the ordinary differential equations (ODEs)
Since the MDM has been used for solving various equations in mathematics and physics [2,3,4], boundary value problems [5,6,7,8,9], various problems in engineering [10,11,12,13], and initial-value problems [14,15,16,17]
Summary
Singular nonlinear partial differential equations (PDEs) arise in various physical phenomena in applied sciences and engineering from such areas as fluid mechanics and heat transfer, Riemannian geometry, applied probability, mathematical physics, and biology. Since the MDM has been used for solving various equations in mathematics and physics [2,3,4], boundary value problems [5,6,7,8,9], various problems in engineering [10,11,12,13], and initial-value problems [14,15,16,17]. Wazwaz et al [20] used the ADM to handle the integral form of the Lane-Emden equations with initial values and boundary conditions.
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