17 research outputs found
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
Wave dynamics on networks: method and application to the sine-Gordon equation
We consider a scalar Hamiltonian nonlinear wave equation formulated on
networks; this is a non standard problem because these domains are not locally
homeomorphic to any subset of the Euclidean space. More precisely, we assume
each edge to be a 1D uniform line with end points identified with graph
vertices. The interface conditions at these vertices are introduced and
justified using conservation laws and an homothetic argument. We present a
detailed methodology based on a symplectic finite difference scheme together
with a special treatment at the junctions to solve the problem and apply it to
the sine-Gordon equation. Numerical results on a simple graph containing four
loops show the performance of the scheme for kinks and breathers initial
conditions.Comment: 31 pages, 9 figures, 2 tables, 41 references. Other author's papers
can be downloaded at http://www.denys-dutykh.com