Results 151 to 160 of about 1,452 (183)

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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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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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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Adaptive Underrelaxation of Picard Iterations in Ground Water Models

Groundwater, 2007
Abstract This methods note examines the use of adaptive underrelaxation of Picard iterations to accelerate the solution convergence for nonlinear ground water flow problems. Ground water problems are nonlinear when drains, phreatophytes, stream aquifer, and similar features are simulated.
Timothy, Durbin, David, Delemos
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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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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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On the quaternion Julia sets via Picard–Mann iteration

Nonlinear Dynamics, 2023
Krzysztof Gdawiec, Ricardo Fariello
exaly