A difference scheme for Cauchy problem for the hyperbolic equation with self-adjoint operator

作者：Ashyralyev Allaberen; Koksal Mehmet Emir; Agarwal Ravi P^*

来源：Mathematical and Computer Modelling, 2010, 52(1-2): 409-424.

DOI：10.1016/j.mcm.2010.03.012

• Abstract hyperbolic equation
• Difference scheme
• Initial-value problem
• Numerical solution
• Stability

A new second order absolutely stable difference scheme is presented for Cauchy problem for second-order hyperbolic differential equations containing the operator A(t). this scheme makes use of this operator which is unbounded linear self-adjoint positive definite with domain in an arbitrary Hilbert space. The stability estimates for the solution of this difference scheme and for the first and second-order difference derivatives are established. The theoretical statements for the solution of this difference scheme are supported by the results of numerical experiments.

• 出版日期2010-7