Variable order step size algorithm for solving second order ODEs

• Main Authors: Rasedee, Ahmad Fadly Nurullah, Abdul Sathar, Mohamad Hassan, Wong, Tze Ji, Koo, Lee Feng
• Other Authors: Asbullah, Muhammad Asyraf
• Format: Book Section
• Language: English
• Published: UPM Press 2019
• Online Access: http://psasir.upm.edu.my/id/eprint/79017/1/2019-chapterinbookvariablenocover.pdf; http://psasir.upm.edu.my/id/eprint/79017/
• Institution: Universiti Putra Malaysia

Previous multi step method using a divided difference formulation for solving higher order ordinary differential equations (ODEs) requires calculating the integration co-efficients at every step. In the current research, a multi step method in backwards difference form is established. The backward difference formulation offers a solution to the tedious calculation of integration coefficients. Rather than calculating inte-gration coefficients at every step change, a backward difference formulation requires calculating integration coefficients only once in the beginning and if required once more at the end. The proposed method will also be equipped with a variable order step size algorithm to reduce computational cost (calculation time). Both linear and nonlinear second order ODEs will used to validate the accuracy and efficiency of the proposed method.