Lecturer and Junior Researcher in Mathematics. Studied B.Sc. Mathematics at Adamawa State University, Mubi, Adamawa State- Nigeria (Class of 2019), and M.Sc. Mathematical Sciences at AIMS (Class of 2024). Supervisors: Prof. Nourridine Siewe, Dr. Joshua A. K., Prof. Joshua Sunday, Dr. Asabe Ibrahim, and Dr. Danjuma Samaila. Phone: +2348103783521 Address: Kantin Tijjani, Wuro-Patuji, Mubi South, Adamawa State -Nigeria.
This research examines the general step k − block approach for solving higher order oscillatory d... more This research examines the general step k − block approach for solving higher order oscillatory differential equations using Linear Block Approach (LBA). The basic properties of the new method such as order, error constant, zero-stability, consistency, convergence, linear stability and region of absolute stability were also analyzed and satisfied. Some distinct fourth order oscillatory differential equation were directly applied on the new method in order to overcome the setbacks in reduction method, where the step size varies. The results obtained were compared with those in literature and the new method takes away the burden of solving fourth order oscillatory differential equations. The accuracy of the new method proved to be better as it outperformed those of existing methods. Therefore, from the results, the new method has shown better accuracy and faster convergence graphically. One of the advantage of the new method is that it does not require much computational burden and it is also self-starting.
The manuscript proposed a physical application of single step block method using the interpolatio... more The manuscript proposed a physical application of single step block method using the interpolation and collocation procedure for the direct solution second order physical oscillatory initial value problem. The properties of the new method which include error constant, order, zero-stability, consistency and convergent are established and satisfied. The new method was tested on some second order oscillatory initial value problems and compared with the existing works in literature, and later the new method revealed its superiority by producing less error if compared. Therefore, the new method does not required much computation when compared with predictor corrector methods.
This research examines the general step k − block approach for solving higher order oscillatory d... more This research examines the general step k − block approach for solving higher order oscillatory differential equations using Linear Block Approach (LBA). The basic properties of the new method such as order, error constant, zero-stability, consistency, convergence, linear stability and region of absolute stability were also analyzed and satisfied. Some distinct fourth order oscillatory differential equation were directly applied on the new method in order to overcome the setbacks in reduction method, where the step size varies. The results obtained were compared with those in literature and the new method takes away the burden of solving fourth order oscillatory differential equations. The accuracy of the new method proved to be better as it outperformed those of existing methods. Therefore, from the results, the new method has shown better accuracy and faster convergence graphically. One of the advantage of the new method is that it does not require much computational burden and it is also self-starting.
The manuscript proposed a physical application of single step block method using the interpolatio... more The manuscript proposed a physical application of single step block method using the interpolation and collocation procedure for the direct solution second order physical oscillatory initial value problem. The properties of the new method which include error constant, order, zero-stability, consistency and convergent are established and satisfied. The new method was tested on some second order oscillatory initial value problems and compared with the existing works in literature, and later the new method revealed its superiority by producing less error if compared. Therefore, the new method does not required much computation when compared with predictor corrector methods.
Uploads
Papers by Silas Daniel