Asymptotic Stability of Neutral Differential Systems with Variable Delay and Nonlinear Perturbations Adeleke Timothy Ademola, Adebayo Aderogba, Opeoluwa Lawrance Ogundipe, Gbenga Akınbo, Babatunde Oluwaseun Onasanya Mathematical Sciences and Applications E Notes, 2024 In this paper, the problem of asymptotic stability of a kind of nonlinear perturbed neutral differential system with variable delay is discussed. The Lyapunov-Krasovskii functional constructed, is used to obtain conditions for asymptotic stability of the nonlinear perturbed neutral differential system in terms of linear matrix inequality (LMI). The two new results (delay-independent and delay-dependent criteria) include and extend the existing results in the literature. Finally, an example of delay-dependent criteria is supplied and the simulation result is shown to justify the effectiveness and reliability of the used techniques.
Finite difference spectral collocation schemes for the solutions of boundary value problems A.O. Adewumi, A.A. Aderogba, S.O. Akindeinde, O.O. Fabelurin, R.S. Lebelo Heliyon, 2024 This article introduces novel numerical approaches utilizing both standard and nonstandard finite difference methods to solve one-dimensional Bratu's problems. Using the quasilinearization technique, the original problem is converted into a sequence of linear problems. Chebyshev polynomials are employed to approximate the second derivative of the function y \( x \) , after which Sumudu transform is applied to obtain a new form of trial function. The obtained trial function is then substituted into a linearized and discretized Bratu's equations. We discuss the convergence of the schemes and compare the numerical outcomes to those derived using other relevant methods. We further modify one of the new schemes and apply it to solve boundary value problem with associated Robin conditions. The results show that the proposed schemes yield accurate approximations to the solutions of the problems considered.
Boundedness and asymptotic Behaviour of Solutions of some second-order nonlinear stochastic differential equations with delay S. J. Olaleye, A. A. Aderogba, A. T. Ademola, O. A. Adesina Proyecciones, 2023 This paper considers a certain second-order nonlinear stochastic differential equation with delay. Novel conditions for the existence of solutions that are uniformly bounded and ultimately bounded are obtained. Moreover, we also study the asymptotic behaviour of solutions for the considered equation. We employ Lyapunov’s second method via an appropriate complete Lyapunov functional to achieve these. Obtained results are new, and they improve and complement some existing relatively recent results in the literature. Finally, an example is provided to illustrate the obtained results.
Some finite difference methods to model biofilm growth and decay: Classical and non-standard Yusuf Olatunji Tijani, Appanah Rao Appadu, Adebayo Abiodun Aderogba Computation, 2021 The study of biofilm formation is undoubtedly important due to micro-organisms forming a protected mode from the host defense mechanism, which may result in alteration in the host gene transcription and growth rate. A mathematical model of the nonlinear advection–diffusion–reaction equation has been studied for biofilm formation. In this paper, we present two novel non-standard finite difference schemes to obtain an approximate solution to the mathematical model of biofilm formation. One explicit non-standard finite difference scheme is proposed for biomass density equation and one property-conserving scheme for a coupled substrate–biomass system of equations. The nonlinear term in the mathematical model has been handled efficiently. The proposed schemes maintain dynamical consistency (positivity, boundedness, merging of colonies, biofilm annihilation), which is revealed through experimental observation. In order to verify the accuracy and effectiveness of our proposed schemes, we compare our results with those obtained from standard finite difference schemes and earlier known results in the literature. The proposed schemes (NSFD1 and NSFD2) show good performance. The NSFD2 scheme reveals that the processes of biofilm formation and nutritive substrate growth are intricately linked.
Classical and multisymplectic schemes for linearized kdv equation: Numerical results and dispersion analysis Adebayo Abiodun Aderogba, Appanah Rao Appadu Fluids, 2021 We construct three finite difference methods to solve a linearized Korteweg–de-Vries (KdV) equation with advective and dispersive terms and specified initial and boundary conditions. Two numerical experiments are considered; case 1 is when the coefficient of advection is greater than the coefficient of dispersion, while case 2 is when the coefficient of dispersion is greater than the coefficient of advection. The three finite difference methods constructed include classical, multisymplectic and a modified explicit scheme. We obtain the stability region and study the consistency and dispersion properties of the various finite difference methods for the two cases. This is one of the rare papers that analyse dispersive properties of methods for dispersive partial differential equations. The performance of the schemes are gauged over short and long propagation times. Absolute and relative errors are computed at a given time at the spatial nodes used.
A hybrid collocation method for solving highly nonlinear boundary value problems A.O. Adewumi, S.O. Akindeinde, A.A. Aderogba, B.S. Ogundare Heliyon, 2020 In this article, a hybrid collocation method for solving highly nonlinear boundary value problems is presented. This hybrid method combines Chebyshev collocation method with Laplace and differential transform methods to obtain approximate solutions of some highly nonlinear two-point boundary value problems of ordinary differential equations. The efficiency of the method is demonstrated by applying it to ordinary differential equations modelling Darcy-Brinkman-Forchheimer momentum problem, laminar viscous flow problem in a semi-porous channel subject to transverse magnetic field, fin problem with a temperature-dependent thermal conductivity, transformed equations modelling two-dimensional viscous flow problem in a rectangular domain bounded by two moving porous walls and two-dimensional constant speed squeezing flow of a viscous fluid between two approaching parallel plates. The results obtained are compared with the existing methods and the results show that the new method is quite reasonable, accurate and efficient.
Coupling finite volume and nonstandard finite difference schemes for a singularly perturbed Schrödinger equation A.A. Aderogba, M. Chapwanya, J. Djoko Kamdem, J.M.-S. Lubuma International Journal of Computer Mathematics, 2016 The Schrödinger equation is a model for many physical processes in quantum physics. It is a singularly perturbed differential equation where the presence of the small reduced Planck's constant makes the classical numerical methods very costly and inefficient. We design two new schemes. The first scheme is the nonstandard finite volume method, whereby the perturbation term is approximated by nonstandard technique, the potential is approximated by its mean value on the cell and the complex dependent boundary conditions are handled by exact schemes. In the second scheme, the deficiency of classical schemes is corrected by the inner expansion in the boundary layer region. Numerical simulations supporting the performance of the schemes are presented.
Numerical approach for the solution of oscillatory 1D Schrödinger equation 9th South African Conference on Computational and Applied Mechanics Sacam 2014, 2014
