Journal•ISSN: 0898-1221

# Computers & Mathematics With Applications

Elsevier BV

About: Computers & Mathematics With Applications is an academic journal published by Elsevier BV. The journal publishes majorly in the area(s): Nonlinear system & Finite element method. It has an ISSN identifier of 0898-1221. Over the lifetime, 12895 publications have been published receiving 303441 citations. The journal is also known as: Computers and mathematics with applications.

Topics: Nonlinear system, Finite element method, Boundary value problem, Discretization, Mathematics

##### Papers published on a yearly basis

##### Papers

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TL;DR: The main purpose of this paper is to introduce the basic notions of the theory of soft sets, to present the first results of the the theory, and to discuss some problems of the future.

Abstract: The soft set theory offers a general mathematical tool for dealing with uncertain, fuzzy, not clearly defined objects. The main purpose of this paper is to introduce the basic notions of the theory of soft sets, to present the first results of the theory, and to discuss some problems of the future.

3,759 citations

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TL;DR: A dual method is proposed which decouples the difficulties relative to the functionals f and g from the possible ill-conditioning effects of the linear operator A and leads to an efficient and simply implementable algorithm.

Abstract: For variational problems of the form Inf v∈ V {f(Av)+g(v)} , we propose a dual method which decouples the difficulties relative to the functionals f and g from the possible ill-conditioning effects of the linear operator A. The approach is based on the use of an Augmented Lagrangian functional and leads to an efficient and simply implementable algorithm. We study also the finite element approximation of such problems, compatible with the use of our algorithm. The method is finally applied to solve several problems of continuum mechanics.

2,500 citations

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TL;DR: The authors define equality of two soft sets, subset and super set of a soft set, complement of asoft set, null soft set and absolute soft set with examples and De Morgan's laws and a number of results are verified in soft set theory.

Abstract: In this paper, the authors study the theory of soft sets initiated by Molodtsov. The authors define equality of two soft sets, subset and super set of a soft set, complement of a soft set, null soft set, and absolute soft set with examples. Soft binary operations like AND, OR and also the operations of union, intersection are defined. De Morgan's laws and a number of results are verified in soft set theory.

2,114 citations

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TL;DR: In this paper, the authors used MQ as the spatial approximation scheme for parabolic, hyperbolic and the elliptic Poisson's equation, and showed that MQ is not only exceptionally accurate, but is more efficient than finite difference schemes which require many more operations to achieve the same degree of accuracy.

Abstract: This paper is the second in a series of investigations into the benefits of multiquadrics (MQ). MQ is a true scattered data, multidimensional spatial approximation scheme. In the previous paper, we saw that MQ was an extremely accurate approximation scheme for interpolation and partial derivative estimates for a variety of two-dimensional functions over both gridded and scattered data. The theory of Madych and Nelson shows for the space of all conditionally positive definite functions to which MQ belongs, a semi-norm exists which is minimized by such functions. In this paper, MQ is used as the spatial approximation scheme for parabolic, hyperbolic and the elliptic Poisson's equation. We show that MQ is not only exceptionally accurate, but is more efficient than finite difference schemes which require many more operations to achieve the same degree of accuracy.

1,914 citations

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TL;DR: In this article, the authors presented a powerful, enhanced multiquadrics (MQ) scheme developed for spatial approximations, which is a true scattered data, grid free scheme for representing surfaces and bodies in an arbitrary number of dimensions.

Abstract: We present a powerful, enhanced multiquadrics (MQ) scheme developed for spatial approximations. MQ is a true scattered data, grid free scheme for representing surfaces and bodies in an arbitrary number of dimensions. It is continuously differentiable and integrable and is capable of representing functions with steep gradients with very high accuracy. Monotonicity and convexity are observed properties as a result of such high accuracy. Numerical results show that our modified MQ scheme is an excellent method not only for very accurate interpolation, but also for partial derivative estimates. MQ is applied to a higher order arbitrary Lagrangian-Eulerian (ALE) rezoning. In the second paper of this series, MQ is applied to parabolic, hyperbolic and elliptic partial differential equations. The parabolic problem uses an implicit time-marching scheme whereas the hyperbolic problem uses an explicit time-marching scheme. We show that MQ is also exceptionally accurate and efficient. The theory of Madych and Nelson shows that the MQ interpolant belongs to a space of functions which minimizes a semi-norm and gived credence to our results.

1,744 citations