189 research outputs found
Numerical investigation of Differential Biological-Models via GA-Kansa Method Inclusive Genetic Strategy
In this paper, we use Kansa method for solving the system of differential
equations in the area of biology. One of the challenges in Kansa method is
picking out an optimum value for Shape parameter in Radial Basis Function to
achieve the best result of the method because there are not any available
analytical approaches for obtaining optimum Shape parameter. For this reason,
we design a genetic algorithm to detect a close optimum Shape parameter. The
experimental results show that this strategy is efficient in the systems of
differential models in biology such as HIV and Influenza. Furthermore, we prove
that using Pseudo-Combination formula for crossover in genetic strategy leads
to convergence in the nearly best selection of Shape parameter.Comment: 42 figures, 23 page
Numerical methods for time-fractional evolution equations with nonsmooth data: a concise overview
Over the past few decades, there has been substantial interest in evolution
equations that involving a fractional-order derivative of order
in time, due to their many successful applications in
engineering, physics, biology and finance. Thus, it is of paramount importance
to develop and to analyze efficient and accurate numerical methods for reliably
simulating such models, and the literature on the topic is vast and fast
growing. The present paper gives a concise overview on numerical schemes for
the subdiffusion model with nonsmooth problem data, which are important for the
numerical analysis of many problems arising in optimal control, inverse
problems and stochastic analysis. We focus on the following aspects of the
subdiffusion model: regularity theory, Galerkin finite element discretization
in space, time-stepping schemes (including convolution quadrature and L1 type
schemes), and space-time variational formulations, and compare the results with
that for standard parabolic problems. Further, these aspects are showcased with
illustrative numerical experiments and complemented with perspectives and
pointers to relevant literature.Comment: 24 pages, 3 figure
Shifted Jacobi spectral collocation method with convergence analysis for solving integro-differential equations and system of integro-differential equations
This article addresses the solution of multi-dimensional integro-differential equations (IDEs) by means of the spectral collocation method and taking the advantage of the properties of shifted Jacobi polynomials. The applicability and accuracy of the present technique have been examined by the given numerical examples in this paper. By means of these numerical examples, we ensure that the present technique is simple and very accurate. Furthermore, an error analysis is performed to verify the correctness and feasibility of the proposed method when solving IDE
A M\"untz-Collocation spectral method for weakly singular volterra integral equations
In this paper we propose and analyze a fractional Jacobi-collocation spectral
method for the second kind Volterra integral equations (VIEs) with weakly
singular kernel . First we develop a family of fractional
Jacobi polynomials, along with basic approximation results for some weighted
projection and interpolation operators defined in suitable weighted Sobolev
spaces. Then we construct an efficient fractional Jacobi-collocation spectral
method for the VIEs using the zeros of the new developed fractional Jacobi
polynomial. A detailed convergence analysis is carried out to derive error
estimates of the numerical solution in both - and weighted
-norms. The main novelty of the paper is that the proposed method is
highly efficient for typical solutions that VIEs usually possess. Precisely, it
is proved that the exponential convergence rate can be achieved for solutions
which are smooth after the variable change for a
suitable real number . Finally a series of numerical examples are
presented to demonstrate the efficiency of the method
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