New Stable Numerical Inversion of Generalized Abel Integral Equation
A direct technique for the solution of generalized Abel integral equation numerically which is based on Bernstein polynomials multiwavelets-based approximations is presented. The Bernstein polynomials properties and arrangement of Bernstein polynomials multiwavelets are displayed. In our technique, Bernstein multiwavelets-based operational matrices diminish the taken generalized Abel integral equation to algebraic equation system for less demanding calculations. The solidness and precision are checked by comparing the ascertained approximated solution and the known analytical solution, so the proposed strategy is a steady technique for applying to test information with noise. A few numerical cases with figures are solved to indicate convergence and utilization of our strategy.
KeywordsBernstein polynomials Multiwavelets Abel integral equation
- 1.Zeilon N (1924) Sur Quelques Points de la Theorie de l’Equation Integraled Abel. Arkiv Mat Astr Fysik 18:1–19Google Scholar
- 7.Gakhov FD (1966) Boundary value problems. Oxford University Press, Oxford, London, Edinburg, New York, Paris, Frankfurt, pp 531–535Google Scholar
- 8.Tricomi FG (1985) Integral equations. Dover PublicationsGoogle Scholar
- 11.Singh VK, Pandey RK, Singh OP (2009) New stable numerical solution of singular integral equations of Abel type by using normalized Bernstein polynomials. Appl Math Sci 3:241–255Google Scholar