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We study approximation of non-autonomous linear differential equations with variable delay over infinite intervals. We use piecewise constant argument to obtain a corresponding discrete difference equation. The study of numerical…
A high-frequency recovered fully discrete low-regularity integrator is constructed to approximate rough and possibly discontinuous solutions of the semilinear wave equation. The proposed method, with high-frequency recovery techniques, can…
Partial differential equations have a wide range of applications in modeling multiple physical, biological, or social phenomena. Therefore, we need to approximate the solutions of these equations in computationally feasible terms. Nowadays,…
This paper investigates a numerical probabilistic method for the solution of some semilinear stochastic partial differential equations (SPDEs in short). The numerical scheme is based on discrete time approximation for solutions of systems…
Quasi steady state assumptions are often used to simplify complex systems of ordinary differential equations in modelling of biochemical processes. The simplified system is designed to have the same qualitative properties as the original…
Similarity reductions and new exact solutions are obtained for a nonlinear diffusion equation. These are obtained by using the classical symmetry group and reducing the partial differential equation to various ordinary differential…
Approximation techniques have been historically important for solving differential equations, both as initial value problems and boundary value problems. The integration of numerical, analytic and perturbation methods and techniques can…
We describe a neural-based method for generating exact or approximate solutions to differential equations in the form of mathematical expressions. Unlike other neural methods, our system returns symbolic expressions that can be interpreted…
A method is presented for calculating solutions to differential equations analytically for a variety of problems in physics. An iteration procedure based on the recently proposed BLUES (Beyond Linear Use of Equation Superposition) function…
In this paper we present an efficient numerical approach based on the Renormalization Group method for the computation of self-similar dynamics. The latter arise, for instance, as the long-time asymptotic behavior of solutions to nonlinear…
This paper reports on recent work to compute the asymptotic solution of a n-th order ordinary differential equation. Symbolic methods are used to compute the asymptotics over a large region. Application is made to the computation of the…
We consider the problem of parameter estimation for a system of ordinary differential equations from noisy observations on a solution of the system. In case the system is nonlinear, as it typically is in practical applications, an analytic…
Delay differential equations are of great importance in science, engineering, medicine and biological models. These type of models include time delay phenomena which is helpful for characterising the real-world applications in machine…
In this paper, we introduce a novel numerical approach for approximating the SIR model in epidemiology. Our method enhances the existing linearization procedure by incorporating a suitable relaxation term to tackle the transcendental…
Computational methods for fractional differential equations exhibit essential instability. Even a minor modification of the coefficients or other entry data may switch good results to the divergent. The goal of this paper is to suggest the…
In the paper titled "New numerical approach for fractional differential equations" by A. Atangana and K.M. Owolabi [Math. Model. Nat. Phenom., 13(1), 2018], it is presented a method for the numerical solution of some fractional differential…
We propose a technique for reformulation of state and parameter estimation problems as that of matching explicitly computable definite integrals with known kernels to data. The technique applies for a class of systems of nonlinear ordinary…
Multivariate global polynomial approximations - such as polynomial chaos or stochastic collocation methods - are now in widespread use for sensitivity analysis and uncertainty quantification. The pseudospectral variety of these methods uses…
We rigorously investigate the convergence of a new numerical method, recently proposed by the authors, to approximate the reproduction numbers of a large class of age-structured population models with finite age span. The method consists in…
Understanding dynamics in complex systems is challenging because there are many degrees of freedom, and those that are most important for describing events of interest are often not obvious. The leading eigenfunctions of the transition…