A review of current studies on complexity of algorithms for partial differential equations

@inproceedings{Khalil1976ARO,
  title={A review of current studies on complexity of algorithms for partial differential equations},
  author={H. Khalil and D. L. Ulery},
  booktitle={ACM '76},
  year={1976}
}
We review current work in analytic computational complexity of sequential algorithms for partial differential equations. Included are studies which analyze and compare classes of algorithms for hyperbolic, elliptic and parabolic problems. Emphasis is on the criteria and techniques used to perform the analysis and comparisons. 
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References

SHOWING 1-10 OF 48 REFERENCES
Theory of optimal algorithms
Motivations for studying computational complexity are discus* recent results in algebraic and analytic computational complexity This report is based on an invited paper presented at a Conference forExpand
Comparison of accurate methods for the integration of hyperbolic equations
Historically, second order accurate difference methods have been used for computations in dynamic meteorology and oceanography. We investigate more accurate difference methods and show that fourthExpand
The Direct Solution of the Discrete Poisson Equation in $O(N^2 )$ Operations
An algorithm is described which solves the discrete Poisson equation on a rectangle with a regular $N \times N$ mesh in $O(N^2 )$ arithmetic operations. However, the method is very highly unstable,Expand
Complexity Bounds for Regular Finite Difference and Finite Element Grids
Sharp lower bounds are obtained for multiplications and storage in the sparse system arising from the application of finite difference or finite element techniques to linear boundary value problemsExpand
Comparing certain classes of difference and finite element methods for a hyperbolic problem
The notion of the intervals per wavelength necessary to yield certain prescribed error levels per period is used to compare the computational efficiency of three classes of spatial differencesExpand
A conjugate gradient approach to nonlinear elliptic boundary value problems in irregular regions
Abstract : A version of the conjugate gradient method is proposed for solving discrete approximations to nonlinear elliptic boundary value problems over irregular regions. The convergence rate isExpand
The Relative Efficiency of Finite Difference and Finite Element Methods. I: Hyperbolic Problems and Splines
The finite element method, using smooth splines as basis functions, applied to the model problem $u_t = cu_x $ with periodic data generates a differential-difference equation whose phase error isExpand
Development, evaluation and selection of methods for elliptic partial differential equations
We present a framework within which to evaluate and compare computational methods to solve elliptic partial differential equations. We then report on the results of comparisons of some classicalExpand
Comparison of some fourth order difference schemes for hyperbolic problems
Our purpose is the comparison of a few difference schemes for application to hyperbolic equations such as those found in computational fluid dynamics. In order to provide a valid comparison we willExpand
ON THE SOLUTION OF LARGE SYSTEMS OF LINEAR ALGEBRAIC EQUATIONS WITH SPARSE, POSITIVE DEFINITE MATRICES
Publisher Summary This chapter provides an overview on the solution of large systems of linear algebraic equations with sparse, positive definite matrices. It discusses the current status ofExpand
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