Numerical solution of second-order two-dimensional hyperbolic equation by bi-cubic B-spline collocation method

Bi-Finite Difference Method to Solve Second-Order Nonlinear Hyperbolic Telegraph Equation in Two Dimensions

“…Root mean square error and relative error for equal grid sizes h x � h y � 0.1 and Δτ � 0.01 are calculated at different time levels, as shown in Table 3. Comparison of obtained results with results of other methods in [19,20] display that our numerical results are effective. Figure 4 appears the surface plots of numerical and exact solution at τ � 2 for h x � h y � 0.05 and Δτ � 0.001.…”

“…Keeping Δτ � 0.01, Table 1 presents L 2 , L ∞ errors and relative error for equal grid sizes h x � h y � 0.1, while Table 2 shows the same errors for different grid sizes h x � 0.1 and h y � 0.2 at different time levels. Our results are compared with the obtained results in [19,20]. Obviously, our numerical results are preferable.…”

“…For δ > 0 and c > 0, we consider the following second-order nonlinear hyperbolic telegraph equation in two dimensions on region R (x, y): x ∈ [0, 1], y ∈ [0, 1] fV ττ V xx + V yy − 2δV τ − c 2 V + G(x, y, τ, V)or temporal coordinate with seconds τ > 0 [20]:…”

“…Many authors solved two-dimensional linear hyperbolic equations [14][15][16][17][18]. Two-dimensional nonlinear hyperbolic equations of second order are studied using modi ed B-spline method [19], bicubic B-spline method [20], meshless local and stronge forms [21], and high-order di erence schemes [22]. Smith introduced nite di erence methods [23].…”

Pseudo-Hiperbolik Telegraf Kısmi Diferansiyel Denklemin Modifiye Çift Laplace Metodu ile Çözümü

“…(Latifizadeh, 2013) de, telegraf denkleminin sayısal çözümü için Sinc-colocation metodunu yaklaşık olarak uygulandı. Telegraf denkleminin sayısal çözümlerine yaklaşmak için Cubic B-spline Collocation Metodu kullanıldı (Arora ve Singh, 2020). Telegraf denklemlerinin yaklaşık çözümü için Fibonacci Polinomları yaklaşımı çalışıldı (Kurt ve Yalçınbaş, 2016).…”