Legendre-Galerkin method for the nonlinear Volterra-Fredholm integro-differential equations

The study of solving nonlinear integro-differential equations in Volterra-Fredholm type presents in this paper. The proposed method tends to use Legendre polynomials as a basis in the Galekin method to obtain the numerical solution. We use the Newton method to get the numerical solution of the nonlinear equations resulted from applying the Galerkin method. The comparison of the present study with the existing results in the literature shows an excellent agreement. Numerical examples explain the convergence, applicability, and efficiency of algorithm.

Legendre-Galerkin Method, Dynamical System, and Optimal Control for Solving Covid-19 Model

The advancement of numerical demonstrating of irresistible illnesses is a key examination territory in different fields including the nature and the study of disease transmission. One point of these models is to comprehend the elements of conduct in irresistible infections. For the new strain of Covid (Coronavirus), there is no immunization to secure individuals and to forestall its spread up until now. All things being equal, control procedures related to medical services, for example, social separating, isolation, travel limitations, can be adjusted to control the pandemic of Coronavirus. This article reveals insights into the dynamical practices of nonlinear Coronavirus models dependent on strategy: the Legendre-Galerkin strategy. We summon a novel sign stream chart that is utilized to depict the Coronavirus model. Based on the Legendre-Galerkin method, the covid-19 model. Mathematica, as one of the world's leading computational software, was employed for the implementation of solutions. The proposed numerical techniques provide are excellent. Through our numerical investigations, it is uncovered that social removing between possibly tainted people who are conveying the infection and solid people can diminish or intrude on the spread of the infection. The mathematical reenactment results are insensible concurrence with the investigation forecasts. The free balance and dependability focus for the Coronavirus model is researched. Likewise, the presence of a consistently steady arrangement is demonstrate.

Chebyshev-Legendre Spectral Domain Decomposition Method for Two-Dimensional Vorticity Equations

We extend the Chebyshev-Legendre spectral method to multi-domain case for solving the two-dimensional vorticity equations. The schemes are formulated in Legendre-Galerkin method while the nonlinear term is collocated at Chebyshev-Gauss collocation points. We introduce proper basis functions in order that the matrix of algebraic system is sparse. The algorithm can be implemented efficiently and in parallel way. The numerical analysis results in the case of one-dimensional multi-domain are generalized to two-dimensional case. The stability and convergence of the method are proved. Numerical results are given.