On numerical solutions of telegraph, viscous, and modified Burgers equations via Bernoulli collocation method

The presented work aims to develop a novel technique for obtaining the solution of linear and nonlinear Partial Differential Equations (PI)Ks). This technique is based on applying a collocation method with the aid of Bernoulli polynomials and the nse of snch an algorithm to solve different types of PDEs. The method applies the regular finite difference scheme to the main problem and transforms it into an algebraic system. The obtained system is then solved, the unknown coefficient is acquired, and an approximate solution for the problems is achieved. Some test results of famous equations, including the telegraph, viscous Burger, and modified Burger equations, are tested to ensure that the provided algorithm is effective and robust. In addition, a comparison is provided with other recent techniques from the literature. The current technique proves to have high accuracy concerning the error measure and through graphical representation of the solution.