Evolutionary numerical approach for solving nonlinear singular periodic boundary value problems

Abstract

In this approximation study, a nonlinear singular periodic model in nuclear physics is solved by using the Hermite wavelets (HW) technique coupled with a numerical iteration technique such as the Newton Raphson (NR) one for solving the resulting nonlinear system. The stimulation of offering this numerical work comes from the aim of introducing a consistent framework that has as effective structures as Hermite wavelets. Two numerical examples of the singular periodic model in nuclear physics have been investigated to observe the robustness, proficiency, and stability of the designed scheme. The proposed outcomes of the HW technique are compared with available numerical solutions that established fitness of the designed procedure through performance evaluated on a multiple execution.

Numerical Simulation of Time Fractional BBM-Burger Equation Using Cubic B-Spline Functions

“…Using Equation (21) in Equation ( 14), we have By putting values of χ 0 , χ 1 , χ 2 and G 1 , G 2 , G 3 and after simplification, we have where Z ⋆ , Z ⋆⋆ , and γ were defined above. If augment factor jΨ ℘+1 j ≤ 1, then the suggested scheme will be stable.…”

“…So, several investigations have been done in recent years to determine the numerical solution of water wave model (see, for example, [14,15] and the references therein). Researchers introduced many different methods to develop an approximate analytical solution for the fractional differential equation and systems, such as the cubic B-spline method (CBS) by [16,17] and homotopy analysis method (HAM) by [18], unified method (UM) [19], Runge-Kutta method [20], Hermite wavelet technique together with Newton Raphson iteration method [21], and Lie symmetry method [22]. The time fractional Benjamin-Bona-Mahony-Burger (BBM-Burger) equation was proposed to discuss the dynamic physical system.…”

Nonlinear Schrodinger Equations with Variable Coefficients: Numerical Integration

“…Many other evolution equations such as time-fractional Benjamin-Bona Mahony equation (TFBBM) [17], (3 + 1)-dimensional extended date-Jimbo-Kashiwara-Miwa equation [18], Bruta-Gelfand equation [19], and similar boundary value problems arising from an adiabatic tubular chemical reactor theory [20], nuclear physics [21], and magneto-hydrodynamics incompressible nanofluid flow past over an infinite rotating disk [22] have been solved using different analytical and numerical approaches [17] applied the integrating factor property to obtain analytical solution of TFBBM equation after reducing the equation to nonlinear fractional ordinary differential equation using its Lie symmetry. In [18], a new exact Lump-soliton solution that localized in all spatio-temporal directions was derived using Hirota method.…”

Comprehensive review of numerical schemes based on Hermite wavelets

“…After the approval of many theories to be ready for mathematical implementation, Discrete Hermite Wavelet Transform was utilized in image processing by Abdulrahman et al [20]. Mohammed et al [21] designed a novel Hermite wavelets (HW) technique to solve nonlinear singular periodic boundary value problems. A proficient solver for the coupled system of fractional differential equations (FDEs) is illustrated by Khader & Babatin [22].…”