Name
Abstract | ||
|---|---|---|
Summary. To solve 1D linear integral equations on bounded intervals with nonsmooth input functions and solutions, we have recently
proposed a quite general procedure, that is essentially based on the introduction of a nonlinear smoothing change of variable
into the integral equation and on the approximation of the transformed solution by global algebraic polynomials. In particular,
the new procedure has been applied to weakly singular equations of the second kind and to solve the generalized air foil equation
for an airfoil with a flap. In these cases we have obtained arbitrarily high orders of convergence through the solution of
very-well conditioned linear systems. In this paper, to enlarge the domain of applicability of our technique, we show how
the above procedure can be successfully used also to solve the classical Symm's equation on a piecewise smooth curve. The
collocation method we propose, applied to the transformed equation and based on Chebyshev polynomials of the first kind, has
shown to be stable and convergent. A comparison with some recent numerical methods using splines or trigonometric polynomials
shows that our method is highly competitive.
|
Year | DOI | Venue |
|---|---|---|
2000 | 10.1007/PL00005414 | Numerische Mathematik |
Keywords | Field | DocType |
numerical quadrature,integral equation,numerical method,order of convergence,chebyshev polynomial,comparative study,galerkin method,hilbert space,collocation method,linear system,linear equation | Chebyshev polynomials,Linear equation,Mathematical optimization,Nonlinear system,Polynomial,Mathematical analysis,Integral equation,Numerical analysis,Collocation method,Mathematics,Piecewise | Journal |
Volume | Issue | ISSN |
86 | 4 | 0029-599X |
Citations | PageRank | References |
0 | 0.34 | 2 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| G. Monegato | 1 | 64 | 17.11 |
| L. Scuderi | 2 | 22 | 4.92 |