LAUSR

Abstract Numerical solution of time-dependent differential equations with quasi-interpolation usually uses derivatives of a quasi-interpolant directly to approximate corresponding spatial derivatives (called the direct technique) in equations. This in turn requires that the quasi-interpolant should possess high-order derivatives for solving high-order differential equations. In addition, the resulting numerical solution usually gives a lower approximation accuracy. To circumvent these limitations, the paper proposes a new scheme for getting high-order numerical solutions of time-dependent differential equations based on quasi-interpolation. The scheme uses an iterated technique instead of the direct quasi-interpolation technique for approximating spatial derivatives. Moreover, it requires only computing the first-order derivative of the involved quasi-interpolant. Numerical examples of solving several benchmark equations using the proposed scheme are provided at the end of the paper to demonstrate these features vividly.