A super accurate shifted Tau method for numerical computation of the Sobolev-type differential equation with nonlocal boundary conditions

Analysis of higher order difference method for a pseudo-parabolic equation with delay

“…In [1] authors considered the explicit finite difference method for quasilinear DPPEs and proved that the fully discrete scheme is absolutely stable and convergent of order two in space and of order one in time variable. In [22] a super accurate numerical scheme to solve the one-dimensional Sobolev type partial differential equation with an initial and two nonlocal integral boundary conditions is considered. This methods are based on the shifted Standard and shifted Chebyshev Tau method.…”

On solving fractional logistic population models with applications

“…Saadatmandi and Dehghan (2006) used the tau method for the one-dimensional parabolic inverse problem, while the authors in Ahmadabadi and Dastjerdi (2016) applied the tau approximation for solving the weakly singular Volterra integral equation. Soltanalizadeh et al (2014) introduced a new method based on the tau approximation for the Sobolev-type differential equation with nonlocal boundary conditions. In Pourgholi et al (2017), the authors considered the Legendre wavelets as basis of the spectral tau approximation to solve integral equations, while Pishbin (2017) applied an operational tau technique for solving systems of integro-differential equations.…”

A RBF partition of unity collocation method based on finite difference for initial–boundary value problems

“…Brill [8] and Showalter [48] established the existence of solutions of semilinear evolution equations of Sobolev type in Banach space, while the global solvability and blow-up of equations of Sobolev type were considered in [2]. Numerically, a lot of simulation methods have been developed for pseudo-parabolic equations [62,46], but most of the existing works are based on the classical FE methods [47,30], FD schemes [50], or FV element methods [60] as discretization tools.…”

“…Comparison between RBF-PUM-FD and RBF-FD[24] using IMQ for the pseudo-parabolic equation: MAE, CPU time (in seconds) and CN for Halton points with δt = 0.001 and T = 1. 46. × 10 −3 26.68 6.59 × 10 +03 9.85 2.13 × 10 −2 182.26 2.90 × 10 +17 40 5 8.80 1.25 × 10 −3 55.61 7.60 × 10 +04 11.75 1.29 × 10 −2 531.12 5.52 × 10 +18…”