Objective The main purpose of this paper is to present an accelerated nonstandard finite difference method for solving the singularly perturbed Burger-Huxley equation in order to produce more accurate solutions. Results The quasilinearization technique is used to linearize the nonlinear term. A nonstandard methodology of Mickens procedure is used in the spatial direction and also within the first order temporal direction that construct the first-order finite difference approximation to solve the considered problem numerically. To accelerate the rate of convergence from first to second-order, the Richardson extrapolation technique is applied. Numerical experiments were conducted to support the theoretical results.

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This paper introduces a new dimension of an additive functional equation and obtains its general solution. The main goal of this study is to examine the Ulam stability of this equation in IFN-spaces (intuitionistic fuzzy normed spaces) with the help of direct and fixed point approaches and 2-Banach spaces. Also, we use an appropriate counterexample to demonstrate that the stability of this equation fails in a particular case.

In this paper, an implicit finite difference scheme is presented to solve one dimensional unsteady singularly perturbed Burger-Huxley equation. The quadratically convergent quasilinearization technique is used to linearize the nonlinear term of the equation. The innovative significance of this paper is the procedure to consider initial guesses in order to start the quasilinearization technique. This basic initial guessing causes to produce a more accurate solutions with the small iteration number for the problem under consideration. The derivatives are replaced by finite difference approximation, then we obtain the two-level time direction and the three-term recurrence relation in the spatial direction. The convergence analysis of the proposed method has been established. Numerical experiments were conducted to support the theoretical results. Further, the result shows that the proposed method gives a more accurate solution with a higher rate of convergence than some existing methods.

In this paper, we introduce the λ -quadratic functional equation with three variables and obtain its general solution. The main aim of this work is to examine the Ulam-Hyers stability of this functional equation in non-Archimedean Banach space by using direct and fixed point techniques and examine the stability results in non-Archimedean random normed space.