scholarly journals A laguerre-legendre spectral-element method for the solution of partial differential equations on infinite domains: Application to the diffusion of tumour angiogenesis factors

2005 ◽  
Vol 41 (10) ◽  
pp. 1171-1192 ◽  
Author(s):  
J. Valenciano ◽  
M.A.J. Chaplain
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Spectral Element Method ◽  
Spectral Element ◽  
Tumour Angiogenesis ◽  
Partial Differential ◽  
Infinite Domains ◽  
Angiogenesis Factors ◽  
Legendre Spectral Element Method ◽  
Element Method

AN EXPLICIT SUBPARAMETRIC SPECTRAL ELEMENT METHOD OF LINES APPLIED TO A TUMOUR ANGIOGENESIS SYSTEM OF PARTIAL DIFFERENTIAL EQUATIONS

2004 ◽  
Vol 14 (02) ◽  
pp. 165-187 ◽  
Author(s):  
J. VALENCIANO ◽  
M. A. J. CHAPLAIN
Keyword(s):  
Steady State ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Numerical Solution ◽  
Spectral Element Method ◽  
Method Of Lines ◽  
Spectral Element ◽  
Tumour Angiogenesis ◽  
Partial Differential ◽  
Element Method

In this paper we consider a numerical solution to Anderson and Chaplain's tumour angiogenesis model1 over two-dimensional complex geometry. The numerical solution of the governing system of non-linear evolutionary partial differential equations is obtained using the method of lines: after a spatial semi-discretisation based on the subparametric Legendre spectral element method is performed, the original system of partial differential equations is replaced by an augmented system of stiff ordinary differential equations in autonomous form, which is then advanced forward in time using an explicit time integrator based on the fourth-order Chebyshev polynomial. Numerical simulations show the convergence of the steady state numerical solution towards the linearly stable steady state analytical solution.

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