Consider the scheme (12) for the nonlinear wave equation
Chapter 8, Problem 9(choose chapter or problem)
Consider the scheme (12) for the nonlinear wave equation (10). Let the discrete energy be dened asEn r =1 2 jvn+1 j vn j t 2 + 1 2 jvn+1 j+1 vn+1 j r vn j+1 vn j r +1 4 j vn+1 j 2 +vn j2+ 1 16 jvn+1 j 8 +vn j8( jr)6 .Bymultiplying(12)by 1 2(vn+1 j vn1 j ),showthat En = En1.Concludethat En does not depend on n.
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