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Table 1 A list of stable hybrid schemes where U(t) is interpolated by using the Lag-(3,0) scheme and its derivatives by a wider stencil

From: On hybrid temporal basis functions for stable numerical solution of time domain boundary integral equations

Hybrid schemes denoted as

Eigenvalue

Temporal

Resolution

Errors

(L2 norm (43))

(M,N)- (M1,N1)- (M2,N2)

analysis

ωΔt=π/12

ωΔt=π/8

ωΔt=π/6

ωΔt=π/4

Lag-(3,0)-(3,0)-(3,0)

Stable

0.00533780

0.01995454

0.04894223

0.15217784

Lag-(3,0)-(4,0)-(4,0)

Stable

0.00091520

0.00389055

0.01211062

0.09690772

Lag-(3,0)-(4,0)-(5,0)

Stable

0.00106346

0.00413456

0.01189096

0.05654576

Opt-(3,0)-(5,0)-(5,0)

Stable

0.00114423

0.00392707

0.00700110

0.01436286

  1. Also shown are the errors in L2 norm for the example presented in Section 7