A Second Order Accurate Difference Method for Systems of Hyperbolic Partial Differential Equations.
BROWN UNIV PROVIDENCE R I DIV OF ENGINEERING
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A second order accurate difference method is presented for systems of first order hyperbolic differential equations. The method is analogous to the Courant, Isaacson, Rees CIR method, except that the error introduced in one time step is 0delta t cubed instead of 0delta t squared as is the case for the CIR method. Convergence of the proposed method is established. The cumulative error at a fixed time is shown to be 0delta t squared. The proposed method is compared with several other second order accurate methods by considering in detail the special case of the system of equations governing flexural wave propagation in elastic beams. These comparisons indicate that the proposed method has substantial advantages over the other methods considered in that the method is computationally stable for larger mesh sizes. As a result, less computing time is required to obtain solutions with a given accuracy. Author
- Numerical Mathematics