Rational approximation with cuckoo search algorithm for multifarious Painlevé type differential equations

Abstract This endeavor aims to present a new comprehensive technique to compute the approximate solutions of Painleve type differential equations (P-type-DE) with arbitrary order. The purpose is achieved by the idea of combining rational approximation with the cuckoo search algorithm (RACS). The cuckoo search algorithm (CSA) is mainly a meta-heuristic optimization technique inspired by the brood parasitism of cuckoo birds. It utilizes Levy flights for the searching procedure with few controlling variables, which makes its global search capacity extremely robust to optimize the objective function. Here, the key role of the objective function is played by the fitness function of P-type-DE, which is structured by a trial solution having unknown weights. Furthermore, a comparative study is also conducted among the calculated results, the exact and other reference solutions, which demonstrates the rightness and computational intelligence of RACS for the non-linear differential equations of arbitrary order.