Numerical Approximation of the 3rd Order Pseudo-Parabolic Equation Using Collocation Technique

This study aims to numerically approximate the solution of third-order pseudo-parabolic partial differential equations (PDEs), which exhibit both parabolic and hyperbolic characteristics. To achieve this, the cubic trigonometric tension B-spline collocation technique is employed for spatial discretization, while the finite difference method (FDM) is used for time discretization. The precision and consistency of the proposed numerical method are analyzed through the approximation of two illustrative examples, demonstrating its accuracy and reliability. A stability analysis, conducted using the von Neumann method, confirms that the method is unconditionally stable. The results show that the method effectively manages large-scale problems, with the numerical solution remaining bounded over time for the considered equations.