
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’.
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
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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