Nonlinear differential equations extensively used mathematical models for many interesting and important phenomena observed in numerous areas of science and technology. They are inspired by problems in diverse fields such as economics, biology, fluid dynamics, physics, differential geometry, engineering, control theory, materials science, and quantum mechanics. This special issue aims to highlight recent developments in methods and applications of nonlinear differential equations. In addition, there are papers analyzing equations that arise in engineering, classical and fluid mechanics, and finance. In this paper, we present a new numerical approach, which is concerned with the solutions of Nonlinear Differential Equations determined by a new approximation system based on inverse Laplace transforms using Chebyshev polynomials functional matrix of integration. The obtained solutions are novel, and previous literature lacks such derivations. The reliability and accuracy of our approach were shown by comparing our derived solutions with solutions obtained by other existing methods. The efficiency of the proposed numerical technique is exhibited through graphical illustrations and results drafted in tabular form for specific values of the parameters to validate the numerical investigation. The system capability is clarified through several standard nonlinear differential equations: Duffing, Van der Pol, Blasius, and Haul. The numerical results illustrate that the estimated result is in good agreement with exact or numerical styles available in literature whenever the exact results are unknown. Errors estimation to the corresponding numerical scheme also is carried out.

In this paper a novel technique implementing

In this paper, the solution of Hammerstein integral equations is presented by a new approximation method based on operational matrices of Chebyshev polynomials. The nonlinear Hammerstein and Volterra Hammerstein integral equations are reduced to a system of nonlinear algebraic equations by using operational matrices of Chebyshev polynomials. Illustrative examples are presented to test the method. The method is less complicated in comparison to others. The results obtained are demonstrated with previously validated results.

No abstract

No abstract