Convergence of Numerical Method for Solving Hyperbolic Equation

In this parer,we investigate the convergence of explicit schemes for solving hyperbolic equations. Traditionally, the well-known (CFL)(Couryant-Friedrichs-Lewy)condition imposes a restriction on the ratio of step size, specifically k h≤C where k is time step-size and h is the spatial step size. This is crucial for ensuring the convergence of the explicit differffence scheme. We focus on a hyperbolic equation defined over domain 0 ≤ x < ∞ and 0 ≤ t ≤ tfwith boundary condition defined as u(x,t) = f(x,t).In this study,we will demonstrate that nude certain conditions. the numerical solution obtained from the difference scheme converge to the true solution without aforementioned restriction on the step size ratio k h. Our results contribute to the understanding of explicit scheme in the numerical method for hyperbolic equation,offeringpotential improvements in the practical computations.