Numerical algorithm for the solution of third order differential equations in orthogonal hybrid function (HF) domain

The present work proposes a new set of orthogonal hybrid functions (HF) which evolved from synthesis of orthogonal sample-and-hold functions (SHF) and triangular functions (TF). The HF set is used to approximate a time function in a piecewise linear manner. The algorithm of one-shot operational matrices for integration of different orders in HF domain are derived and employed for more accurate multiple integration and solution of third order non-homogeneous differential equations. The results are compared with the exact solution and the results obtained via 4^th order Runge-Kutta method.