Vector collocation-Tau Method for linear partial differential equations

✍ Scribed by John C Mason; G Oluremi Olaofe

• Publisher: Elsevier Science
• Year: 1988
• Tongue: English
• Weight: 345 KB
• Volume: 11
• Category: Article
• ISSN: 0895-7177
• DOI: 10.1016/0895-7177(88)90574-2

✦ Synopsis

A bivariate polynomial approximation method is described for the solution of linear partial differential equations based on the "se of the tau method in the first independent variable and a collocation method in the second.

The method has the advantage over bivariate tau methods that coefficients in the differential equation do not need to be expressible or expandable as polynomials in the second variable. Moreover the method reduces to a tau method for determining a set of coefficient vectors for the polynomial approximation, and the resulting linear algebraic system may be solved efficiently in O(r123) operations, where m and n are the respective degrees in ce and y of the polynomial approximation.

lKeywords:

Bivariate, Chebyshev Polynomials, Collocation, Partial Differential Equations, Tau Method 20n leave of absence from the Mathematics