The general implicit-block method with two-points and extra derivatives for solving fifth-order ordinary differential equations

Document Type : Research Paper


1 Department of Mathematics, College of Education for Pure Sciences, University of Anbar, Iraq

2 Department of Mathematics, College of Computer Science and Mathematics, University of Kufa, Najaf, Iraq

3 Information Technology Research and Development Center (ITRDC), University of Kufa, Najaf, Iraq


In this work, a general implicit block method (GIBM) with two points for solving general fifth-order initial value problems (IVPs) has been derived. GIBM is proposed by adopting the basis functions of Hermite interpolating polynomials. GIBM is presented to be suitable with the numerical solutions of fifth-order IVPs. Hence, the derivation of GIBM has been introduced. Numerical implementations compared with the existing numerical GRKM method are used to prove the accuracy and efficiency of the proposed GIBM method. The impressive numerical results of the test problems using the proposed GIBM method agree well with the approximated solutions of them using the existing GRKM method.