We develop a robust uniformly convergent numerical scheme for singularly perturbed time dependent Burgers-Huxley partial differential equation. We first discretize the time derivative of the equation using the Crank-Nicolson finite difference method. Then, the resulting semi-discretized nonlinear ordinary differential equations are linearized using the quasilinearization technique, and finally, design a fitted Operator upwind finite difference method to resolve the layer behavior of the solution in the spatial direction. Our analysis has shown that the presented method is second order parameter uniform convergent in time and first order in space. Numerical experiments are conducted to validate the theoretical results.

In this paper, we introduce and study fuzzy variational-like inclusion, fuzzy resolvent equation and H (0,0)- f-h accretive Operator in real uniformly smooth Banach spaces. It is established that fuzzy variational-like inclusion is equivalent to a fixed point problem as well as to a fuzzy resolvent equation. This equivalence is used to define an iterative algorithm for solving fuzzy resolvent equation. Some examples are given.

In this paper,  a  one-dimensional modified Burgers'  equation is considered for different  Reynolds numbers. For very high Reynolds numbers,  the solution possesses a multiscale character in some part of the independent domain and thus can be classified as a  singularly perturbed problem. A numerical scheme that uses a fitted Operator finite difference scheme to solve the spatial derivatives and the implicit Euler scheme for the time derivative is proposed to solve the modified  Burgers'  equation via Rothe's method. It is important to note that the proposed fitted Operator finite difference scheme is based on the midpoint upwind scheme. The stability of the scheme is established and the error associated with each discretisation is estimated. Numerical simulations are carried out to validate the theoretical findings.

This paper provides sufficient conditions that guarantee the existence of positive solutions to a boundary value problem of a nonlinear fractional differential equation on the half line. Our analysis takes advantage of a theory on cones and mixed monotone Operators combined with the diagonalization method. The paper also contains some examples that are numerically solved by the Adomian Decomposition Method.