Computational schemes between the exact, analytical and numerical solution in present of time—fractional ecological model

Abstract

This paper investigates the accuracy of three recent computational schemes (the extended simplest method (ESEM), sech—tanh expansion method (STEM), and modified Kudryashov method (MKM)) through calculating the absolute value of error between their solutions and numerical solutions. The computational schemes claim to obtain exact traveling wave solutions of the investigated models; therefore, it supposes the numerical study for any models that have been analytically investigated under any constructed computational solutions that will be matching, but our study shows a different fact. (Khater et al Soft Computing (Submitted)) has studied the computational solutions of the time-fractional Lotka—Volterra (LV) model through the above-mentioned computational schemes. Many solutions have been obtained in different mathematical formulas such as exponential, trigonometric, hyperbolic, etc. These solutions describe the interaction between the high -frequency Langmuir and the low-frequent ion-acoustic waves with many applications in electromagnetic waves, plasma physics, and signal processing through optical fibers, coastal engineering, and fluid dynamics. This manuscript applies the trigonometric quintic B—spline scheme to the fractional LV model along with the Caputo and Fabrizio fractional derivatives and computational obtained solutions for investigating the numerical solutions under each employed analytical scheme. The numerical solutions are simulated in two-dimensional sketches to explain the relation between exact and numerical solutions. This study proves the computational fact hypotheses for obtaining exact solutions, and they all obtain computational solutions.