70 research outputs found
New parameter-uniform discretisations of singularly perturbed Volterra integro-differential equations
We design and analyse two numerical methods namely a fitted mesh and a fitted operator finite difference methods for
solving singularly perturbed Volterra integro-differential equations. The fitted mesh method we propose is constructed using a finite
difference operator to approximate the derivative part and some suitably chosen quadrature rules for the integral part. To obtain a
parameter-uniform convergence, we use a piecewise-uniform mesh of Shishkin type. On the other hand, to construct the fitted operator
method, the Volterra integro-differential equation is discretised by introducing a fitting factor via the method of integral identity with
the use of exponential basis function along with interpolating quadrature rules [2]. The two methods are analysed for convergence and
stability. We show that the two methods are robust with respect to the perturbation parameter. Two numerical examples are solved to
show the applicability of the proposed schemes
On the numerical integration of singularly perturbed Volterra integro-differential equations
Magister Scientiae - MScEfficient numerical approaches for parameter dependent problems have been an inter-
esting subject to numerical analysts and engineers over the past decades. This is due
to the prominent role that these problems play in modeling many real life situations
in applied sciences. Often, the choice and the e ciency of the approaches depend on
the nature of the problem to solve. In this work, we consider the general linear first-order singularly perturbed Volterra integro-differential equations (SPVIDEs). These
singularly perturbed problems (SPPs) are governed by integro-differential equations
in which the derivative term is multiplied by a small parameter, known as "perturbation parameter". It is known that when this perturbation parameter approaches
zero, the solution undergoes fast transitions across narrow regions of the domain
(termed boundary or interior layer) thus affecting the convergence of the standard
numerical methods. Therefore one often seeks for numerical approaches which preserve stability for all the values of the perturbation parameter, that is "numerical
methods. This work seeks to investigate some "numerical methods that have been
used to solve SPVIDEs. It also proposes alternative ones. The various numerical
methods are composed of a fitted finite difference scheme used along with suitably
chosen interpolating quadrature rules. For each method investigated or designed, we
analyse its stability and convergence. Finally, numerical computations are carried
out on some test examples to con rm the robustness and competitiveness of the
proposed methods
The linear barycentric rational method for a class of delay Volterra integro-differential equations
A method for solving delay Volterra integro-differential equations is introduced. It is based on two applications of linear barycentric rational interpolation, barycentric rational quadrature and barycentric rational finite differences. Its zero–stability and convergence are studied. Numerical tests demonstrate the excellent agreement of our implementation with the predicted convergence orders
A numerical method for a second order singularly perturbed Fredholm integro-differential equation
The boundary-value problem for a second order singularly perturbed Fredholm integro-differential equation was considered in this paper. For the numerical solution of this problem, we use an exponentially fitted difference scheme on a uniform mesh which is succeeded by the method of integral identities with the use of exponential basis functions and interpolating quadrature rules with the weight and remainder terms in integral form. Also, the method is first order convergent in the discrete maximum norm. Numerical example shows that recommended method has a good approximation characteristic.WOS:0006611395000042-s2.0-8510854604
Abstract book
Welcome at the International Conference on Differential and Difference Equations
& Applications 2015.
The main aim of this conference is to promote, encourage, cooperate, and bring
together researchers in the fields of differential and difference equations. All areas
of differential & difference equations will be represented with special emphasis on
applications. It will be mathematically enriching and socially exciting event.
List of registered participants consists of 169 persons from 45 countries.
The five-day scientific program runs from May 18 (Monday) till May 22, 2015
(Friday). It consists of invited lectures (plenary lectures and invited lectures in
sections) and contributed talks in the following areas:
Ordinary differential equations,
Partial differential equations,
Numerical methods and applications, other topics
List of contents
Rev. iberoam. bioecon. cambio clim. Vol.1(1) 2015; 95-114Los cambios medioambientales globales hacen pensar en un aumento futuro de la aridez, por ello es necesario buscar alternativas que permitan un uso más eficiente del agua y reducir su consumo, teniendo en cuenta que es un recurso limitado. En la actualidad, aproximadamente el 59,7% del total de agua planificada para todos los usos en Cuba se utiliza en la agricultura, pero no más del 50% de esa agua se convierte directamente en productos agrícolas. El estudio de las funciones agua-rendimiento y su uso dentro de la planificación del agua para riego es una vía importante para trazar estrategias de manejo que contribuyan al incremento en la producción agrícola. Utilizando los datos de agua aplicada por riego y los rendimientos obtenidos en más de 100 experimentos de campo realizados fundamentalmente en suelo Ferralítico Rojo de la zona sur de La Habana y con ayuda de herramientas de análisis de regresión en este trabajo se estiman las funciones agua aplicada-rendimientos para algunos cultivos agrícolas y se analizan las posibles estrategias de optimización del riego a seguir en función de la disponibilidad de agua. Seleccionar una estrategia de máxima eficiencia del riego puede conducir a reducciones de agua a aplicar entre un 21,6 y 46,8%, incrementos de la productividad del agua entre 17 y 32% y de la relación beneficios/costo estimada de hasta un 3,4%. Lo anterior indica la importancia desde el punto de vista económico que puede llegar a alcanzar el uso de esta estrategia en condiciones de déficit hídrico. El conocimiento de las funciones agua aplicada por riego-rendimiento y el uso de la productividad del agua, resultan parámetros factibles de introducir como indicadores de eficiencia en el planeamiento del uso del agua en la agricultura, con lo cual es posible reducir los volúmenes de agua a aplicar y elevar la relación beneficio-costo actual.Rev. iberoam. bioecon. cambio clim. Vol.1(1) 2015; 95-11
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