Results 201 to 210 of about 3,362 (237)

On the speed of convergence of Picard iterations of backward stochastic differential equations

Probability, Uncertainty and Quantitative Risk, 2022
Hutzenthaler M, Kruse T, Nguyen TA. On the speed of convergence of Picard iterations of backward stochastic differential equations. Probability, Uncertainty and Quantitative Risk.
Martin Hutzenthaler, Thomas Kruse, Tuan Anh Nguyen   +2 more
exaly   +2 more sources

Picard Iterations for Solution of Nonlinear Equations in Certain Banach Spaces

Journal of Mathematical Analysis and Applications, 2000
Let E be a real uniformly smooth Banach space and let A: D(A)⊂E↦E be locally Lipschitzian and strongly quasi-accretive. It is proved that a Picard recursion process converges strongly to the unique solution of the equation Ax=f, f∈R(A), with the ...
Chika Moore
exaly   +2 more sources

Approximation of Non-Lipschitz SDEs by Picard Iterations

Applied Mathematical Finance, 2018
International audienceIn this paper, we propose an approximation method based on Picard iterations deduced from the Doléans–Dade exponential formula. Our method allows to approximate trajectories of Markov processes in a large class, e.g.
Emmanuel Lépinette
exaly   +1 more source

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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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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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Chebyshev acceleration of picard-lindelöf iteration

BIT, 1992
This paper complements recent work by \textit{R.D. Skeel} [SIAM J. Sci. Stat. Comput. 10, No. 4, 756-776 (1989; Zbl 0687.65076) and \textit{O. Nevanlinna} [Numer. Math. 57, No. 2, 147-156 (1990; Zbl 0697.65058)] regarding the question as to whether a significant acceleration of waveform iteration (Picard-Lindelöf iteration) is possible.
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Polynomial acceleration of the Picard-Lindelof iteration

IMA Journal of Numerical Analysis, 1998
The effect of polynomial acceleration of the Picard-Lindelöf iteration formula is analyzed for a function \(x(t)\) on a bounded interval. The basic iteration formula for solution to \[ x'(t)+ Ax(t)= f(t),\quad x(0)= x_0,\quad t\in [0,T],\tag{i} \] is \[ x^n= Kx^{n-1}+ g,\quad n=1,2,\dots\quad Kx(t)= \int^t_0 e^{-M(t-s)}Nx(s)ds,\tag{ii} \] \[ g= e^{-Mt ...
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Picard iterations of boundary-layer equations

7th Computational Fluid Dynamics Conference, 1985
A method of solving the boundary-layer equations that arise in singular-perturbation analysis of flightpath optimization problems is presented. The method is based on Picard iterations of the integrated form of the equations and does not require iteration to find unknown boundary conditions.
M. ARDEMA, L. YANG
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Picard Iteration, Chebyshev Polynomials and Chebyshev-Picard Methods: Application in Astrodynamics

The Journal of the Astronautical Sciences, 2013
This paper extends previous work on parallel-structured Modified Chebyshev Picard Iteration (MCPI) Methods. The MCPI approach iteratively refines path approximation of the state trajectory for smooth nonlinear dynamical systems and this paper shows that the approach is especially suitable for initial value problems of astrodynamics.
John L. Junkins, Ahmad Bani Younes, Robyn M. Woollands, Xiaoli Bai   +3 more
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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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