An Efficient Algorithm for Solving Hyperbolic Partial Differential Equations with a Nonlocal Conservation Condition

Abstract

In this paper, a numerical scheme based on the Galerkin method is extended for solving one-dimensional hyperbolic partial differential equations with a nonlocal conservation condition. To achieve this goal, we apply the interpolating scaling functions. The most important advantages of these bases are orthonormality, interpolation, and having flexible vanishing moments. In other words, to increase the accuracy of the approximation, we can individually or simultaneously increase both the degree of polynomials (multiplicity $r$ ) and the level of refinement (refinement level $J$ ). The convergence analysis is investigated, and numerical examples guarantee it. To show the ability of the proposed method, we compare it with existing methods, and it can be confirmed that our results are better than them.