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- Bennewitz, Christer, et al.
(författare)
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A limit point criterion with applications to nonselfadjoint equations
- 2002
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Ingår i: Journal of Computational and Applied Mathematics. - 0377-0427. ; 148:1, s. 257-265
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Tidskriftsartikel (refereegranskat)abstract
- A unified approach is given which allows one to construct examples of all three cases resulting from a generalization of the classical Weyl limit point limit circle analysis, for differential equations as well as for difference equations.
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| 2. |
- Engquist, Björn, et al.
(författare)
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Multi-phase computations in geometrical optics
- 1996
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Ingår i: Journal of Computational and Applied Mathematics. - : Elsevier BV. - 0377-0427 .- 1879-1778. ; 74:1-2, s. 175-192
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Tidskriftsartikel (refereegranskat)abstract
- In this work we propose a new set of partial differential equations (PDEs) which can be seen as a generalization of the classical eikonal and transport equations, to allow for solutions with multiple phases. The traditional geometrical optics pair of equations suffer from the fact that the class of physically relevant solutions is limited. In particular, it does not include solutions with multiple phases, corresponding to crossing waves. Our objective has been to generalize these equations to accommodate solutions containing more than one phase. The new equations are based on the same high frequency approximation of the scalar wave equation as the eikonal and the transport equations. However, they also incorporate a finite superposition principle. The maximum allowed number of intersecting waves in the solution can be chosen arbitrarily, but a higher number means that a larger system of PDEs must be solved. The PDEs form a hyperbolic system of conservation laws with source terms. Although the equations are only weakly hyperbolic, and thus not well-posed in the strong sense, several examples show the viability of solving the equations numerically. The technique we use to capture multivalued solutions is based on a closure assumption for a system of equations representing the moments.
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| 3. |
- Karlberg, Lennart, et al.
(författare)
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Padé type approximants and orthogonal polynomials for Markov-Stieltjes functions : Extrapolation and rational approximation (Luminy, 1989)
- 1990
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Ingår i: Journal of Computational and Applied Mathematics. - 0377-0427 .- 1879-1778. ; 32:1-2, s. 153-157
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Tidskriftsartikel (refereegranskat)abstract
- Padé-type approximants are rational functions with some preassigned poles whose power series expansion coincides with that of a given series as far as possible. The main open question for these approximants is the choice of the poles in order to obtain interesting approximation and convergence results. In this paper, the authors study this problem for functions of the Markov-Stieltjes type, when some of the poles are -1 and +1 with arbitrary multiplicities and points in the union of (-∞,-1) and (1,∞) with even multiplicities.
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| 4. |
- Lenferink, Wilhelmus
(författare)
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A second order scheme for a time-dependent, singularly perturbed convection-diffusion equation
- 2002
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Ingår i: Journal of Computational and Applied Mathematics. - 0377-0427 .- 1879-1778. ; 143:1, s. 49-68
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Tidskriftsartikel (refereegranskat)abstract
- We consider a numerical scheme for a one-dimensional, time-dependent, singularly perturbed convection-diffusion problem. The problem is discretized in space by a standard finite element method on a Bakhvalov-Shishkin type mesh. The space error is measured in an L2 norm. For the time integration, the implicit midpoint rule is used. The fully discrete scheme is shown to be convergent of order 2 in space and time, uniformly in the singular perturbation parameter. © 2002 Elsevier Science B.V. All rights reserved.
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| 8. |
- Aarao, J, et al.
(författare)
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Numerical implementation of the EDEM for modified Helmholtz BVPs on annular domains
- 2011
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Ingår i: JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS. - : Elsevier Science B.V., Amsterdam.. - 0377-0427. ; 235:5, s. 1342-1353
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Tidskriftsartikel (refereegranskat)abstract
- In a recent paper by the current authors a new methodology called the Extended-Domain-Eigenfunction-Method (EDEM) was proposed for solving elliptic boundary value problems on annular-like domains. In this paper we present and investigate one possible numerical algorithm to implement the EDEM. This algorithm is used to solve modified Helmholtz BVPs on annular-like domains. Two examples of annular-like domains are studied. The results and performance are compared with those of the well-known boundary element method (BEM). The high accuracy of the EDEM solutions and the superior efficiency of the EDEM over the BEM, make EDEM an excellent alternate candidate to use in the animation industry, where speed is a predominant requirement, and by the scientific community where accuracy is the paramount objective.
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| 9. |
- Adriani, Andrea, et al.
(författare)
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Asymptotic spectra of large (grid) graphs with a uniform local structure, Part II : Numerical applications
- 2024
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Ingår i: Journal of Computational and Applied Mathematics. - : Elsevier. - 0377-0427 .- 1879-1778. ; 437
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Tidskriftsartikel (refereegranskat)abstract
- In the current work we are concerned with sequences of graphs having a grid geometry, with a uniform local structure in a bounded domain Ω ⊂ Rd , d ≥ 1. When Ω = [0, 1], such graphs include the standard Toeplitz graphs and, for Ω = [0,1]d, the considered class includes d-level Toeplitz graphs. In the general case, the underlying sequence of adjacency matrices has a canonical eigenvalue distribution, in the Weyl sense, and it has been shown in the theoretical part of this work that we can associate to it a symbol f. The knowledge of the symbol and of its basic analytical features provides key information on the eigenvalue structure in terms of localization, spectral gap, clustering, and global distribution. In the present paper, many different applications are discussed and various numerical examples are presented in order to underline the practical use of the developed theory. Tests and applications are mainly obtained from the approximation of differential operators via numerical schemes such as Finite Differences, Finite Elements, and Isogeometric Analysis. Moreover, we show that more applications can be taken into account, since the results presented here can be applied as well to study the spectral properties of adjacency matrices and Laplacian operators of general large graphs and networks, whenever the involved matrices enjoy a uniform local structure.
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| 10. |
- Agram, Nacira, 1987-, et al.
(författare)
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Infinite horizon optimal control of forward–backward stochastic differential equations with delay
- 2014
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Ingår i: Journal of Computational and Applied Mathematics. - : Elsevier. - 0377-0427 .- 1879-1778. ; 259:Part B, s. 336-349
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Tidskriftsartikel (refereegranskat)abstract
- We consider a problem of optimal control of an infinite horizon system governed by forward–backward stochastic differential equations with delay. Sufficient and necessary maximum principles for optimal control under partial information in infinite horizon are derived. We illustrate our results by an application to a problem of optimal consumption with respect to recursive utility from a cash flow with delay.
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