1987
DOI: 10.1002/num.1690030303
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Abstract: A fully Galerkin method in both space and time is developed for the second-order, linear hyperbolic problem. Sinc basis functions are used and error bounds are given which show the exponential convergence rate of the method. The matrices necessary for the formulation of the discrete system are easily assembled. They require no numerical integrations (merely point evaluations) to be filled. The discrete problem is formulated in two different ways and solution techniques for each are described. Consideration of … Show more

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Cited by 16 publications
(11 citation statements)
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“…The Sinc-Galerkin method for partial differential equations has previously been developed for the model elliptic equation in two dimensions [1,9], the parabolic equation in one dimension [7], and the second order hyperbolic equation in one dimension [11]. The present paper extends the method to the steady state problem in three dimensions and the time dependent problems in at least two.…”
Section: Introductionmentioning
confidence: 93%
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“…The Sinc-Galerkin method for partial differential equations has previously been developed for the model elliptic equation in two dimensions [1,9], the parabolic equation in one dimension [7], and the second order hyperbolic equation in one dimension [11]. The present paper extends the method to the steady state problem in three dimensions and the time dependent problems in at least two.…”
Section: Introductionmentioning
confidence: 93%
“…Subject to the growth assumption depending on the spatial dimension, the summation limits and stepsizes in the spatial directions remain as in the elliptic discussion. Appropriate time parameters are given in [11] as follows: (xl ........ I) ..... co(x,~..., . Hence the code needed to construct the vector co(H (4)) or recover U (4) is merely a set of nested loops.…”
Section: S*kl(x Y Z T)=sijk(x Y Z) S~(t)mentioning
confidence: 99%
“…and the weight is taken to be (3.ss) 1 _,'(t) = _ for reasons that are discussed in [4]. As before, integration by parts is used to transfer the differentiation of u onto S'w*.…”
Section: (F G) = _z' F(t)g(t)w*(t)dtmentioning
confidence: 99%
“…Further details concerning the derivation of the system (3.61) can be found in Ref. 4. Note that nonzero initial conditions can be handled in a manner analogous to that used for nonzero boundary conditions in the previous discussion.…”
Section: ( 4 G ) = Jmf(t)g(t)w*(t) D T mentioning
confidence: 99%
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