A novel computing multi-parametric homotopy approach for system of linear and nonlinear Fredholm integral equations

Global Dynamics of a Periodic SEIRS Model with General Incidence Rate

“…For this approximation we have used a Taylor expansion of the periodic solution̂( ); another interesting possibility could be varying the approximation used for R 0 , for example, changing the Taylor approach of̂( ) around = 1 instead of = 0. The graphs of the solutions were obtained with ODE 45 from Matlab, but other methods can be used to improve them, for example, Adomian methods or homotopy methods [24,25]. The Maple code used to estimate R 0 is available for anyone who wants to use it.…”

“…There exist multiple numerical methods to compute and plot the solutions of nonautonomous differential equations; see, for example, the Adomian method, the homotopy analysis method, or the modified homotopy methods (see, e.g., [24,25]). For this work we use Matlab algorithms (ODE 45) to graph the solution of system (76) with these initial conditions.…”

Evolution equations with a parameter and application to transport-convection differential equations

“…For instance, a huge variation can occur in a fraction of a second, causing a major change that may affect the whole system's state forever. Indeed, it has turned out recently that many phenomena in different fields, including sciences, engineering, and technology, can be described very successfully by models using fractional order differential equations [6,7,10,11,13,14,18,21,22,27]. Hence, differential equations with fractional derivatives have become a useful tool for describing nonlinear phenomena that are involved in many branches of chemistry, engineering, biology, ecology, and numerous domains of applied sciences.…”

Laplace Transform Homotopy Perturbation Method for the Two Dimensional Black Scholes Model with European Call Option

“…The solution obtained from HPM converges rapidly to the exact solution. There are many researchers applying HPM to engineering and biological problems [20][21][22][23][24][25][26][27], confirming that HPM has become a potential tool for solving mathematical problems [17]. However, some complicated problems cannot be solved using HPM alone.…”