We transform a double integral into a second-order initial value problem, which we solve using Euler's method and Richardson extrapolation. For an example we consider, we achieve accuracy close to machine precision (~10-13). We find that the algorithm is capable of determinin...
Richardson, S., Vortices, Liouville’s Equation and the Bergman Kernel Function, Mathematika, 1980, vol. 27, no. 2, pp. 321–334. Article MathSciNet Google Scholar Borah, D., Haridas, P., and Verma, K., Comments on the Green’s Function of a Planar Domain, Anal. Math. Phys.,...
Chen and Liu [36] considered an implicit difference scheme for the three-dimensional fractional advection–diffusion equation and applied Richardson extrapolation for improving the accuracy. As we know, the implicit difference methods work well when the size of the problem is not too large. However,...
This algorithm combines the advantages of Lagrangian particle tracking and continuum Euler methods (Andrews and O’Rourke, 1996). The particle volume fraction Θ is calculated from the particle distribution function f (Andrews and O’Rourke, 1996). (5)Θ=∬fmρsdmvwith (6)α+Θ=1, m is ...
Then, we introduce interface operators that allow us to express the domain decomposition algorithm as a Richardson-type iteration on the interface unknowns. Algebraically speaking, the Schwarz algorithm is equivalent to a Jacobi iteration applied to a linear system whose matrix has a block structure....
Then, we introduce interface operators that allow to express the domain decomposition algorithm as a Richardson type iteration on the interface unknowns. Algebraically speaking, the Schwarz algorithm is equivalent to a Jacobi iteration applied to a linear system whose matrix has a block structure. A...
Algorithmequidistribution principlemoving mesh methodRichardson extrapolationsingularly perturbed problemIn this paper, both structural and dynamical stabilities of steady transonic shock solutions for one-dimensional Euler–Poisson systems are investigated. First, a steady transonic shock solution with a super...
In Sect. 5 we propose an algorithm for effective calculation of the numerical solution of the considered boundary value problem. In Sect. 6 we consider the special case \(r=2\), and we provide illustrative numerical examples. In order to compare the proposed method with other existing ones,...