A Class of Block Multi-derivative Numerical Techniques for Singular Advection Equations

Abstract

The integration of some differential equations is hard to acquire because of the presence of singular point(s) in these equations. These equations are best solved by some unique technique. Multi-derivative techniques have a long history of powerful integration of such equations yet till date, a couple of class of this technique has been explored for integrating partial differential equations. This work centers around the development, analysis, and implementation of a class of multi-derivative technique on partial differential equations. The approaches were effectively analyzed and were turned out to be consistent, stable and convergent. Numerical outcomes got likewise demonstrated the approximation quality of the technique over existing techniques in the literature.

Investigating The Behaviourial Analysis Of Disease Transmission Coefficient In SEIRS Epidemic Model With Disease Induced Death

“…However, the continuous coefficients 𝛽 𝑖,𝑗 (𝑡), 𝑖 = 0, 𝑣, 𝑘, 𝑗 = 1(1)𝑘 were determined. Ogunniran (2019) obtained approximation of the exact solution 𝑦(𝑡) by evaluating the function:…”

“…The first formulated model was on smallpox and was introduced by Bernoulli (1760). In this paper, one of the hybrid block methods proposed by Ogunniran (2019) is used for the simulation of the SEIRS model to have an insight in the effect of saturation coefficient of the model. The model classifies individual as susceptible, exposed, infected and recovered.…”

Simulation of the Movement of Groundwater in an Aquifer

“…Section 3 of the study employs an analytical technique [14] to address the issue raised in Section 2. The Fourier series and its properties are used as the principal tool for problem analysis [15,16].…”

Linear Stability Analysis of Runge-Kutta Methods for Singular Lane-Emden Equations

“…A new basic rational approximation method was developed for solving singular initial value problems of ordinary differential equations by Ogunniran & Adeniyi [13]. Ogunniran [14] also developed a class of block multi-derivative numerical integrator for singular advection equations. The solution of Emden-Fowler equations was solved using the variational iteration method by Olayiwola [15].…”