Results 171 to 180 of about 17,865 (205)

Solving Stiff Problems Using Generalized Picard Iterations

AIP Conference Proceedings, 2009
The main point of the talk is an alternative approach to the construction of numerical methods for stiff problems. It can be interpreted as a generalization of fixed‐point iterations for implementation of implicit collocation methods. Proposed algorithms combine easy implementation and low cost of iterations with superior convergence properties on ...
V. V. Bobkov, B. V. Faleichik, P. A. Mandrik, V. I. Repnikov, Theodore E. Simos, George Psihoyios, Ch. Tsitouras   +6 more
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Picard iteration methods for a spherical atmosphere

Journal of Quantitative Spectroscopy and Radiative Transfer, 2009
Several methods for solving the radiative transfer equation in a spherical atmosphere are presented. These methods include the long characteristic Picard iteration, and the conventional and the accelerated short characteristic Picard iteration. Approximate methods as for instance the Picard iteration methods with open boundaries are also discussed. The
Doicu, Adrian, Trautmann, Thomas
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On the Region of Convergence of Picard's Iteration

ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik, 1972
AbstractA new convergence condition is described for Picard's iteration for the boundary value problem where f(t, y, z) is continuous and satisfies a Lipschitz‐condition in y and z. This convergence condition is optimal in a sense specified precisely in this paper.
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Solving differential equations using modified Picard iteration

International Journal of Mathematical Education in Science and Technology, 2010
Many classes of differential equation are shown to be open to solution through a method involving a combination of a direct integration approach with suitably modified Picard iterative procedures. The classes of differential equations considered include typical initial value, boundary value and eigenvalue problems arising in physics and engineering and
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Waveform Iteration and the Shifted Picard Splitting

SIAM Journal on Scientific and Statistical Computing, 1989
The theme of this paper is that the primary computational bottleneck in the solution of stiff ordinary differential equations (ODEs) and the parallel solution of nonstiff ODEs is the implicitness of the ODE rather than the approximation of the integration process (or in conventional terminology, numerical stability rather than accuracy), and therefore ...
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Picard style iteration for anisotropic H-functions

Journal of Quantitative Spectroscopy and Radiative Transfer, 2005
Abstract An iterative approach is used to derive a ‘closed form’ approximation H * for Chandrasekhar's H-function in the general anisotropic case. Numerical results demonstrate a satisfactory accuracy level except in conservative or near conservative cases.
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The Picard–HSS iteration method for absolute value equations

Optimization Letters, 2014
\textit{O. L. Mangasarian} [ibid. 3, No. 1, 101--108 (2009; Zbl 1154.90599)] proposed a generalized Newton method for the absolute value equation (AVE) \(Ax - |x| = b\) and investigated its convergence properties. This paper deals with the convergence of the Picard-HSS iteration method to solve AVE, where \(A\) is a non-symmetric positive definite ...
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Picard’s iterative method for nonlinear advection–reaction–diffusion equations

Applied Mathematics and Computation, 2009
A system of nonlinear partial differential equations of the type \[ u_t(t,x) =F(t,x,u(t,x),\nabla u(t,x),\Delta u(t,x ...
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Modified Picard type iterative algorithm for nonexpansive mappings

2018
Summary: In this paper, we propose a modified version of Picard type iterative algorithm for finding a fixed point of a nonexpansive mapping defined on a closed convex subset of a Hilbert space. We prove the strong convergence of the sequence generated by the proposed algorithm to a fixed point of a nonexpansive map, such fixed point is also a solution
Ansari, Qamrul Hasan, Gursoy, Faik, KARAKAYA, Vatan, Erturk, Muzeyyen   +3 more
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A perturbation-based acceleration for Monte Carlo – Thermal Hydraulics Picard iterations. Part I: Theory and application to extruded BWR unit-cell.

Annals of Nuclear Energy, 2022
Stefano Terlizzi, Dan Kotlyar
exaly