In this paper,  The Picard method is proposed to solve the system of first-order fuzzy  differential equations  $(FDEs)$ with fuzzy initial conditions under generalized $H$-differentiability. Theexistence and uniqueness of the solution and convergence of theproposed method are proved in details. Finally, the method is illustrated by solving some examples.

14 We have implemented the Jacobian-free Newton-Krylov (JFNK) method 15 for solving the first-order ice sheet momentum equation in order to improve 16 the numerical performance of the Community Ice Sheet Model (CISM), the 17 land ice component of the Community Earth System Model (CESM). Our 18 JFNK implementation is based on significant re-use of existing code. For ex19 ample, our physics-based...

A standard method for solving coupled multiphysics problems in light water reactors is Picard iteration, which sequentially alternates between solving single physics applications. This solution approach is appealing due to simplicity of implementation and the ability to leverage existing software packages to accurately solve single physics applications. However, there are several drawbacks in t...

We construct examples of K3 surfaces of geometric Picard rank 1. Our method is a refinement of that of R. van Luijk [vL]. It is based on an analysis of the Galois module structure on étale cohomology. This allows to abandon the original limitation to cases of Picard rank 2 after reduction modulo p. Furthermore, the use of Galois data enables us to construct examples which require significantly ...

We investigate a method proposed by E. Arrondo and J. Caravantes to study the Picard group of a smooth lowcodimension subvariety X in a variety Y when Y is homogeneous. We prove that this method is strongly related to the signature σY of the Poincaré pairing on the middle cohomology of Y . We give under some topological assumptions a bound on the rank of Picard group Pic(X) in terms of σY and r...

We study curves with linear series that are exceptional with regard to their secant planes. Working in the framework of an extension of Brill-Noether theory to pairs of linear series, we prove that a general curve of genus g has no exceptional secant planes, in a very precise sense. We also address the problem of computing the number of linear series with exceptional secant planes in a one-para...

We study the variation of relative cohomology for a pair consisting of a smooth projective hypersurface and an algebraic subvariety in it. We construct an inhomogeneous Picard-Fuchs equation by applying a Picard-Fuchs operator to the holomorphic top form on a Calabi-Yau hypersurface in toric variety, and deriving a general formula for the d-exact form on one side of the equation. We also derive...

The recognition and the calculation of all branches of solutions of the nonlinear boundary value problems is difficult obviously. The complexity of this issue goes back to the being nonlinearity of the problem. Regarding this matter, this paper considers steady state reactive transport model which does not have exact closed-form solution and discovers existence of dual or triple solutions in so...

Our main goal in this paper is to construct the first explicit fundamental domain of the Picard modular group acting on the complex hyperbolic space CH . The complex hyperbolic space is a Hermitian symmetric space, its bounded realization is the unit ball in C equipped with the Bergman metric. The Picard modular group is a discontinuous holomorphic automorphism subgroup of SU(2, 1) with Gaussia...