A Computational Modeling Based on Trigonometric Cubic B-Spline Functions for the Approximate Solution of a Second Order Partial Integro-Differential Equation

Collocation Approach Based on an Extended Cubic B -Spline for a Second-Order Volterra Partial Integrodifferential Equation

“…The suggested approach is implemented on the aforementioned problem to get numerical results. The estimated errors are compared to those provided in [23,[32][33][34] at various time stages in Table 1. Figure 1 presents an efficient comparison of approximate and exact solutions at various time levels.…”

“…The suggested technique is applied on the above problem to acquire approximate solutions and absolute errors. Table 2 reports the contrast between the computed errors of present scheme and those of [32,34] for different time levels. For various time stages, a sharp contrast between exact and approximate solutions is presented in Figure 4.…”

“…The proposed methodology is utilized to acquire the numerical results for this problem. Table 3 shows the effi-ciency of the presented scheme by comparing the errors with those presented in [32,34]. Figures 7 and 8 illustrate the 2D and 3D comparison of the exact to approximate solutions.…”

“…Ali et al [33] developed a quartic B-spline collocation approach for solving PIDEs with a weakly singular kernel. Trigonometric cubic B -spline-based collocation method was used to solve PIDEs by Ali et al [34].…”

Method of Reference Signals Creating in Non-Destructive Testing Based on Low-Speed Impact

“…Interpolation using splines is more efficient than interpolation by polynomials [20], since it gives reliable results even for low degrees of interpolation equations, and the Runge phenomenon that occurs when using high-order polynomial interpolation does not occur. The main advantages of spline interpolation are stability and complexity.…”