Abstract
The aim of this study is to give a good strategy for solving some linear and nonlinear partial differential equations in engineering and physics fields, by combining Laplace transform and the modified variational iteration method. This method is based on the variational iteration method, Laplace transforms, and convolution integral, introducing an alternative Laplace correction functional and expressing the integral as a convolution. Some examples in physical engineering are provided to illustrate the simplicity and reliability of this method. The solutions of these examples are contingent only on the initial conditions.
Highlights
Nonlinear equations are of great importance to our contemporary world
Nonlinear phenomena have important applications in applied mathematics, physics, and issues related to engineering
Two Laplace variational iteration methods are currently suggested by Wu in [10–13]
Summary
Nonlinear equations are of great importance to our contemporary world. Nonlinear phenomena have important applications in applied mathematics, physics, and issues related to engineering. Despite the importance of obtaining the exact solution of nonlinear partial differential equations in physics and applied mathematics, there is still the daunting problem of finding new methods to discover new exact or approximate solutions. Many authors have devoted their attention to study solutions of nonlinear partial differential equations using various methods. Among these attempts are the Adomian decomposition method, homotopy perturbation method, variational iteration method [1–5], Laplace variational iteration method [6–8], differential transform method, and projected differential transform method. The main result of this paper is to introduce an alternative Laplace correction functional and express the integral as a convolution This approach can tackle functions with discontinuities and impulse functions effectively
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