A High-Order Domain Decomposition algorithm for the Heat Equation
نویسندگان
چکیده
To solve the heat equation on parallel computers, a high-order finite difference domain decomposition algorithm is discussed. In this procedure, interface values between subdomains are calculated by the classical explicit scheme, while interior values of sub-domains are determined by the famous forth-order compact scheme. The stability and convergence for this domain decomposition algorithm are proved. The stability bound of the procedure is derived to be 1 + √ 6 3 times that of the classical explicit scheme. And the L-error is proved to be O(τ 2 + h). Numerical examples confirm the third order convergence and indicate that the stability condition is sharp.
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