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Cone invariance and squeezing properties for inertial manifolds for nonautonomous evolution equations

100%

Koksch N., Siegmund S.

Banach Center Publications

2003

tom 60

nr 1

27-48

In this paper we summarize an abstract approach to inertial manifolds for nonautonomous dynamical systems. Our result on the existence of inertial manifolds requires only two geometrical assumptions, called cone invariance and squeezing property, and some additional technical assumptions like boundedness or smoothing properties. We apply this result to processes (two-parameter semiflows) generated by nonautonomous semilinear parabolic evolution equations.

New modification of Maheshwari’s method with optimal eighth order convergence for solving nonlinear equations

81%

Sharifi S., Ferrara M., Salimi M., Siegmund S.

Open Mathematics

2016

tom 14

nr 1

443-451

In this paper, we present a family of three-point with eight-order convergence methods for finding the simple roots of nonlinear equations by suitable approximations and weight function based on Maheshwari’s method. Per iteration this method requires three evaluations of the function and one evaluation of its first derivative. These class of methods have the efficiency index equal to [...] 814≈1.682${8^{{\textstyle{1 \over 4}}}} \approx 1.682$. We describe the analysis of the proposed methods along with numerical experiments including comparison with the existing methods. Moreover, the attraction basins of the proposed methods are shown with some comparisons to the other existing methods.

Ograniczanie wyników

1 Banach Center Publications

1 Open Mathematics

2 Siegmund S.

1 Ferrara M.

1 Koksch N.

1 Salimi M.

1 Sharifi S.

1 2016

1 2003

Wyniki wyszukiwania

Cone invariance and squeezing properties for inertial manifolds for nonautonomous evolution equations

New modification of Maheshwari’s method with optimal eighth order convergence for solving nonlinear equations