SOLVING NON-LINEAR FREDHOLM INTEGRO-DIFFERENTIAL EQUATIONS WITH COMBINED ORTHONORMAL BERNSTEIN AND IMPROVED BLOCK-PULSE FUNCTIONS
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초록
The purpose of this paper is to o er a computational way to solve Fredholm integro-di erential equations (NFIDEs) of nonlinear type using a mixed of polynomials of Bernstein (BPs) and an block- pulse basis functions of improved form. The nonlinear part is approximated using combined BP operational matrices and an improved block pulse function, while the di erential part is approximated using derivative combined BP operational matrices and an improved block pulse func- tion. Finally, a set equations of nonlinear form is obtained by transform- ing the main equation that we solve for the undetermined coecients required to obtain the approximate series solution. Using speci c com- putational examples, we also demonstrate how the operational matrices can be used to solve (NFIDEs).
Abstract
The purpose of this paper is to o er a computational way to solve Fredholm integro-di erential equations (NFIDEs) of nonlinear type using a mixed of polynomials of Bernstein (BPs) and an block- pulse basis functions of improved form. The nonlinear part is approximated using combined BP operational matrices and an improved block pulse function, while the di erential part is approximated using derivative combined BP operational matrices and an improved block pulse func- tion. Finally, a set equations of nonlinear form is obtained by transform- ing the main equation that we solve for the undetermined coecients required to obtain the approximate series solution. Using speci c com- putational examples, we also demonstrate how the operational matrices can be used to solve (NFIDEs).
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