Items related to Lax Equivalence Theorem: Numerical analysis, Finite...

Lax Equivalence Theorem: Numerical analysis, Finite difference method, Partial differential equation, Well- posed problem, Initial value problem, Limit of a sequence - Softcover

 
9786131820823: Lax Equivalence Theorem: Numerical analysis, Finite difference method, Partial differential equation, Well- posed problem, Initial value problem, Limit of a sequence

Synopsis

Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In numerical analysis, the Lax equivalence theorem is the fundamental theorem in the analysis of finite difference methods for the numerical solution of partial differential equations. It states that for a consistent finite difference method for a well-posed linear initial value problem, the method is convergent if and only if it is stable. The importance of the theorem is that while convergence of the solution of the finite difference method to the solution of the partial differential equation is what is desired, it is ordinarily difficult to establish because the numerical method is defined by a recurrence relation while the differential equation involves a differentiable function

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