An Accurate Block Hybrid Collocation Method for Third Order Ordinary Differential Equations

Abstract

The block hybrid collocation method with two off-step points is proposed for the direct solution of general third order ordinary differential equations. Both the main and additional methods are derived via interpolation and collocation of the basic polynomial. These methods are applied in block form to provide the approximation at five points concurrently. The stability properties of the block method are investigated. Some numerical examples are tested to illustrate the efficiency of the method. The block hybrid collocation method is also implemented to solve the nonlinear Genesio equation and the problem in thin film flow.

Symmetric 2-Step 4-Point Hybrid Method for the Solution of General Third Order Differential Equations

“…(8) and its first and second derivatives eqns. (9) and (10), respectively, the following symmetric explicit schemes and their derivatives are also developed by the same procedure for the evaluation of y n+2, y′ n+2 and y″ n+2.…”

“…The direct approach for solving this type of ordinary differential equations have been studied and appeared in different literatures [1][2][3][4][5][6][7]. This direct approach has demonstrated advantages over the popular approach (reduction to system of first order approach) in terms of speed and accuracy [8,9]. Many authors have focused on direct solution of general second order ivps of odes of the form y″=f (t, y, y′)…”

Penyelesaian Terus Persamaan Pembezaan Biasa Peringkat Tiga menggunakan Kaedah Blok Hibrid Kolokasi Diperbaiki

“…Persamaan (1) kerap kali digunakan dalam pemodelan bagi bidang sains, ekonomi dan kejuruteraan seperti gelombang elektromagnet dan aliran graviti. Pendekatan biasa untuk menyelesaikan (1) adalah penurunan peringkat kepada suatu sistem dengan tiga PPB peringkat pertama dan diselesaikan melalui kaedah satu langkah atau multilangkah seperti kaedah Runge-Kutta, kaedah Euler dan kaedah Adams (Yap et al 2014). Namun, kos penilaian dan ralat pangkasan akan ditambah.…”

Application of single step with three generalized hybrid points block method for solving third order ordinary differential equations

“…Reduction approach has been identified to have some drawbacks which include computer burden and alots of human efforts [1,7,10] and [14]. Because of this, many researchers have attempted to solve Equation (1) directly .…”