1,939 research outputs found
Numerical approximations for population growth model by Rational Chebyshev and Hermite Functions collocation approach: A comparison
This paper aims to compare rational Chebyshev (RC) and Hermite functions (HF)
collocation approach to solve the Volterra's model for population growth of a
species within a closed system. This model is a nonlinear integro-differential
equation where the integral term represents the effect of toxin. This approach
is based on orthogonal functions which will be defined. The collocation method
reduces the solution of this problem to the solution of a system of algebraic
equations. We also compare these methods with some other numerical results and
show that the present approach is applicable for solving nonlinear
integro-differential equations.Comment: 18 pages, 5 figures; Published online in the journal of "Mathematical
Methods in the Applied Sciences
Parallel algorithm with spectral convergence for nonlinear integro-differential equations
We discuss a numerical algorithm for solving nonlinear integro-differential
equations, and illustrate our findings for the particular case of Volterra type
equations. The algorithm combines a perturbation approach meant to render a
linearized version of the problem and a spectral method where unknown functions
are expanded in terms of Chebyshev polynomials (El-gendi's method). This
approach is shown to be suitable for the calculation of two-point Green
functions required in next to leading order studies of time-dependent quantum
field theory.Comment: 15 pages, 9 figure
Numerical Methods for the Nonlocal Wave Equation of the Peridynamics
In this paper we will consider the peridynamic equation of motion which is
described by a second order in time partial integro-differential equation. This
equation has recently received great attention in several fields of Engineering
because seems to provide an effective approach to modeling mechanical systems
avoiding spatial discontinuous derivatives and body singularities. In
particular, we will consider the linear model of peridynamics in a
one-dimensional spatial domain. Here we will review some numerical techniques
to solve this equation and propose some new computational methods of higher
order in space; moreover we will see how to apply the methods studied for the
linear model to the nonlinear one. Also a spectral method for the spatial
discretization of the linear problem will be discussed. Several numerical tests
will be given in order to validate our results
Collocation Method using Compactly Supported Radial Basis Function for Solving Volterra's Population Model
In this paper, indirect collocation approach based on compactly supported
radial basis function is applied for solving Volterras population model. The
method reduces the solution of this problem to the solution of a system of
algebraic equations. Volterras model is a non-linear integro-differential
equation where the integral term represents the effect of toxin. To solve the
problem, we use the well-known CSRBF: Wendland3,5. Numerical results and
residual norm 2 show good accuracy and rate of convergence.Comment: 8 pages , 1 figure. arXiv admin note: text overlap with
arXiv:1008.233
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Direct localized boundary-domain integro-differential formulations for physically nonlinear elasticity of inhomogeneous body
A static mixed boundary value problem (BVP) of physically nonlinear elasticity for a continuously inhomogeneous body is considered. Using the two-operator Green-Betti formula and the fundamental solution of an auxiliary linear operator, a non-standard boundary-domain integro-differential formulation of the problem is presented, with respect to the displacements and their gradients. Using a cut-off function approach, the corresponding localized parametrix is constructed to reduce the nonlinear BVP to a nonlinear localized boundary-domain integro-differential equation. Algorithms of mesh-based and mesh-less discretizations are presented resulting in sparsely populated systems of nonlinear algebraic equations
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