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Applied Mathematical Modelling
Article
License: Elsevier Non-Commercial
Data sources: UnpayWall
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Applied Mathematical Modelling
Article . 1981
License: Elsevier Non-Commercial
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Applied Mathematical Modelling
Article . 1981 . Peer-reviewed
License: Elsevier Non-Commercial
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Solution of parabolic partial differential equations

Authors: J. R. Reed; N. Mullineux; M. Heydarian;

Solution of parabolic partial differential equations

Abstract

In their paper, 1 Curran et al. express some reservation concerning the suggestion 2 that the time dependence in parabolic differential equations be removed by taking the Laplace transform. The caution arises from the necessity for numerical inversion which, they feared, could lead to severe problems. It is true that difficulties can present themselves and some of these are discussed 3 as they occur in transmission-line problems. However, the examples taken to illustrate their basic theory cause no such problem as is shown in reworking their problem 2, which could be expected to present difficulties since it has ‘a discontinuity between the initial and boundary conditions’.

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Keywords

Laplace transform method, Laplace transform, Heat equation, Transform methods (e.g., integral transforms) applied to PDEs, Modelling and Simulation, Applied Mathematics, numerical inversion, Spectral, collocation and related methods for boundary value problems involving PDEs, quadrature formula, Numerical methods for integral transforms

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    citations
    This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
    19
    popularity
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    influence
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citations
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
19
Average
Top 10%
Average
hybrid