Homotopy continuation methods (HCMs) can be used to find the solutions
of polynomial equations. The advantages of HCMs over classical methods such as the
Newton and bisection methods are that HCMs are able to resolve divergence and starting
value problems. In this paper, we develop Super Ostrowski-HCM as a technique to
overcome the starting value problem. We compare the performance of this proposed
method with Ostrowski-HCM. The results provide evidence of the superiority of Super
Ostrowski-HCM.
Second order linear two-point boundary value problems were solved using extended cubic B-spline interpolation method. Extended cubic B-spline is an extension of cubic B-spline consisting of one shape parameter, called λ. The resulting approximated analytical solution for the problems would be a function of λ. Optimization of λ was carried out to find the best value of λ that generates the closest fit to the differential equations in the problems. This method approximated the solutions for the problems much more accurately compared to finite difference, finite element, finite volume and cubic B-spline interpolation methods.
Pembinaan model geometri berbantukan komputer (CAGD) dengan titik data yang mempunyai ketakpastian adalah sukar dan mencabar. Dalam kertas ini, pembinaan model splin-B kabur sebagai perwakilan matematik bagi lengkung dengan data ketakpastian menggunakan titik kawalan kabur dan titik kawalan penyahkaburan dibincangkan. Lengkung splin-B kabur atau splin-B penyahkaburan kubik untuk masalah data ketakpastian akan diperihalkan dengan menggunakan kaedah penghampiran splin-B kubik yang ditakrif menerusi titik kawalan kabur dan titik kawalan penyahkaburan. Bagi menyelesaikan masalah mengenai titik data ketakpastian pula, kaedah pengkaburan dan penyahkaburan titik data berkomponen kabur (penyahkaburan) beserta modelnya diperkenalkan. Bagi menguji tahap keberkesanan model, beberapa contoh lengkung simulasi data tersebut juga dibincangkan.