Spectral methods for solving integro-differential equations and bibiliometric analysis

چکیده مقاله

The use of a bibliography of scientific mapping is appropriate when the emphasis on empirical collaborations generates extensive, fragmented and controversial research streams. In this chapter, first, the integro-differential equations are studied at the bibliometric viewpoint. Also, we discuss the application of this class of equations with arbitrary order, in science. Next, we present some numerical methods based on the spectral methods for finding numerical solution of some kind of integro-differential equations, such as fractional integro-differential equations and variable-order fractional partial integro-differential equations. Moreover, in each method, the estimation errors are presented. Some numerical examples are included to demonstrate the validity and applicability of the numerical techniques. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2021.