Orthogonal Hybrid Functions (HF) for Solving Second Order Differential Equations using One-Shot Integration Operational Matrices

The present work employs a new set of orthogonal hybrid functions (HF) generated from the synthesis of orthogonal sample-and-hold functions (SHF) and triangular functions (TF). The one-shot operational matrices for second order integration are derived. These matrices are employed for more accurate second order integration. Finally, these matrices are employed for solving second order non-homogeneous differential equations followed by a numerical example. The results are compared with the exact solution as well as the results obtained via 4th order Runge-Kutta method.