We introduce an orthogonal basis on the square [-1,1] x [-1,1] generated by Legendre polynomials on [-1,1], and define an associated expression for the expansion of a Riemann integrable function. We describe some properties and derive a uniform convergence theorem. We then present several, numerical experiments that indicate that our methods are more efficient and have better convergence results than some other methods.
|Number of pages||14|
|Journal||Numerical Methods for Partial Differential Equations|
|State||Published - Jan 2010|
- Associated expansions
- Error estimate of numerical solutions
- Legendre polynomial
- Orthogonal basis