High-order numerical solution of second-order one-dimensional hyperbolic telegraph equation

What is it about?

The article is concerned with the development of a high-order numerical scheme to solve the second order one-dimensional hyperbolic telegraph equation provided with some initial and Dirichlet boundary conditions. The core of the proposed method is based on the well conditioning of numerical integral operators to produce well-conditioned linear algebraic equations. The theoretical analysis and numerical experiments presented verify the effectiveness, the accuracy, and the exponential convergence of the proposed method. The method is a robust technique, which can be extended to solve a wide range of problems arising in numerous applications.

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Why is it important?

The method is highly accurate and very stable. Moreover, the method can be easily programmed and implemented.

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