PDE Convergence Test Problem: < SSP_Tools.TestProblems.Advection: @(x)sin(4*pi*x) [0, 1] t= > Time Stepping Method: < SSP_Tools.Integrators.MSRK: MSRK 6s3k4pT2.mat priming=RK3 mini_dt_type=compatible, mini_dt_c=1.000000 > Spatial Discretization: < SSP_Tools.Discretizers.Spectral > Testing 10 Testing 14 Testing 20 Testing 24 Testing 30 Testing 34 Testing 40 Testing 44 Convergence Test Results Problem: Advection Equation u_t - -1*u_x = 0 u(x,0)=@(x)sin(4*pi*x) T=1.000000 Spatial Discretization: Spectral Fourier Collocation Method Time-Stepping Method: MSRK 6s3k4pT2.mat ---------------------------------------------------- N | dt | L1Error | L1Order | L2Error | L2Order | LinfError | LinfOrder | 10 | 0.0400 | 1.54e-03 | - | 1.70e-03 | - | 2.29e-03 | - | 14 | 0.0286 | 4.06e-04 | 3.96 | 4.50e-04 | 3.96 | 6.12e-04 | 3.92 | 20 | 0.0200 | 9.80e-05 | 3.99 | 1.09e-04 | 3.98 | 1.48e-04 | 3.99 | 24 | 0.0167 | 4.79e-05 | 3.93 | 5.27e-05 | 3.98 | 7.20e-05 | 3.93 | 30 | 0.0133 | 1.95e-05 | 4.03 | 2.16e-05 | 3.99 | 3.00e-05 | 3.92 | 34 | 0.0118 | 1.18e-05 | 3.99 | 1.31e-05 | 3.99 | 1.83e-05 | 3.97 | 40 | 0.0100 | 6.20e-06 | 3.98 | 6.86e-06 | 3.99 | 9.53e-06 | 4.00 | 44 | 0.0091 | 4.22e-06 | 4.03 | 4.69e-06 | 3.99 | 6.53e-06 | 3.97 | l2_errors = 0.001702651751380 0.000449776511569 0.000108873297543 0.000052666669380 0.000021625486141 0.000013121492375 0.000006857751915 0.000004686984082 PDE Convergence Test Problem: < SSP_Tools.TestProblems.Advection: @(x)sin(4*pi*x) [0, 1] t= > Time Stepping Method: < SSP_Tools.Integrators.MSRK: MSRK 7s4k5pT2.mat priming=RK3 mini_dt_type=compatible, mini_dt_c=1.000000 > Spatial Discretization: < SSP_Tools.Discretizers.Spectral > Testing 10 Testing 14 Testing 20 Testing 24 Testing 30 Testing 34 Testing 40 Testing 44 Convergence Test Results Problem: Advection Equation u_t - -1*u_x = 0 u(x,0)=@(x)sin(4*pi*x) T=1.000000 Spatial Discretization: Spectral Fourier Collocation Method Time-Stepping Method: MSRK 7s4k5pT2.mat ---------------------------------------------------- N | dt | L1Error | L1Order | L2Error | L2Order | LinfError | LinfOrder | 10 | 0.0400 | 8.20e-05 | - | 9.07e-05 | - | 1.33e-04 | - | 14 | 0.0286 | 1.61e-05 | 4.85 | 1.80e-05 | 4.81 | 2.62e-05 | 4.84 | 20 | 0.0200 | 2.82e-06 | 4.88 | 3.17e-06 | 4.86 | 4.52e-06 | 4.93 | 24 | 0.0167 | 1.16e-06 | 4.89 | 1.30e-06 | 4.89 | 1.86e-06 | 4.87 | 30 | 0.0133 | 3.87e-07 | 4.90 | 4.34e-07 | 4.91 | 6.24e-07 | 4.90 | 34 | 0.0118 | 2.09e-07 | 4.92 | 2.34e-07 | 4.93 | 3.36e-07 | 4.94 | 40 | 0.0100 | 9.37e-08 | 4.93 | 1.05e-07 | 4.93 | 1.50e-07 | 4.96 | 44 | 0.0091 | 5.85e-08 | 4.94 | 6.56e-08 | 4.95 | 9.35e-08 | 4.96 | l2_errors = 1.0e-04 * 0.907178097945637 0.179550559026257 0.031701538634674 0.012987567028462 0.004341746163286 0.002343683213641 0.001051119698948 0.000656054591353 PDE Convergence Test Problem: < SSP_Tools.TestProblems.Advection: @(x)sin(4*pi*x) [0, 1] t= > Time Stepping Method: < SSP_Tools.Integrators.MSRK: MSRK 8s3k6pT2.mat priming=RK3 mini_dt_type=compatible, mini_dt_c=1.000000 > Spatial Discretization: < SSP_Tools.Discretizers.Spectral > Testing 10 Testing 14 Testing 20 Testing 24 Testing 30 Testing 34 Testing 40 Testing 44 Convergence Test Results Problem: Advection Equation u_t - -1*u_x = 0 u(x,0)=@(x)sin(4*pi*x) T=1.000000 Spatial Discretization: Spectral Fourier Collocation Method Time-Stepping Method: MSRK 8s3k6pT2.mat ---------------------------------------------------- N | dt | L1Error | L1Order | L2Error | L2Order | LinfError | LinfOrder | 10 | 0.0400 | 1.87e-05 | - | 2.09e-05 | - | 2.76e-05 | - | 14 | 0.0286 | 2.53e-06 | 5.95 | 2.82e-06 | 5.96 | 3.80e-06 | 5.89 | 20 | 0.0200 | 3.02e-07 | 5.96 | 3.34e-07 | 5.98 | 4.55e-07 | 5.95 | 24 | 0.0167 | 1.02e-07 | 5.97 | 1.12e-07 | 5.99 | 1.54e-07 | 5.94 | 30 | 0.0133 | 2.65e-08 | 6.02 | 2.95e-08 | 5.99 | 4.09e-08 | 5.94 | 34 | 0.0118 | 1.25e-08 | 5.99 | 1.39e-08 | 5.99 | 1.93e-08 | 5.97 | 40 | 0.0100 | 4.75e-09 | 5.97 | 5.25e-09 | 5.99 | 7.31e-09 | 5.99 | 44 | 0.0091 | 2.68e-09 | 6.01 | 2.97e-09 | 5.99 | 4.14e-09 | 5.98 | l2_errors = 1.0e-04 * 0.209419792936133 0.028173744425561 0.003339366459406 0.001121126108096 0.000294571714034 0.000139151801270 0.000052539373518 0.000029673839972 PDE Convergence Test Problem: < SSP_Tools.TestProblems.Advection: @(x)sin(4*pi*x) [0, 1] t= > Time Stepping Method: < SSP_Tools.Integrators.MSRK: MSRK 8s4k7pT2.mat priming=RK3 mini_dt_type=compatible, mini_dt_c=1.000000 > Spatial Discretization: < SSP_Tools.Discretizers.Spectral > Testing 10 Testing 14 Testing 20 Testing 24 Testing 30 Testing 34 Testing 40 Testing 44 Convergence Test Results Problem: Advection Equation u_t - -1*u_x = 0 u(x,0)=@(x)sin(4*pi*x) T=1.000000 Spatial Discretization: Spectral Fourier Collocation Method Time-Stepping Method: MSRK 8s4k7pT2.mat ---------------------------------------------------- N | dt | L1Error | L1Order | L2Error | L2Order | LinfError | LinfOrder | 10 | 0.0400 | 2.22e-06 | - | 2.48e-06 | - | 3.47e-06 | - | 14 | 0.0286 | 2.18e-07 | 6.90 | 2.44e-07 | 6.89 | 3.48e-07 | 6.84 | 20 | 0.0200 | 1.88e-08 | 6.86 | 2.07e-08 | 6.91 | 2.99e-08 | 6.88 | 24 | 0.0167 | 5.29e-09 | 6.96 | 5.85e-09 | 6.93 | 8.20e-09 | 7.09 | 30 | 0.0133 | 1.11e-09 | 7.00 | 1.24e-09 | 6.94 | 1.78e-09 | 6.85 | 34 | 0.0118 | 4.65e-10 | 6.95 | 5.21e-10 | 6.95 | 7.45e-10 | 6.96 | 40 | 0.0100 | 1.51e-10 | 6.92 | 1.68e-10 | 6.96 | 2.38e-10 | 7.01 | 44 | 0.0091 | 7.77e-11 | 6.97 | 8.66e-11 | 6.96 | 1.24e-10 | 6.87 | l2_errors = 1.0e-05 * 0.248148148649378 0.024392532401373 0.002071247276360 0.000585405810240 0.000124371727305 0.000052107813632 0.000016821782976 0.000008663731694 PDE Convergence Test Problem: < SSP_Tools.TestProblems.Advection: @(x)sin(4*pi*x) [0, 1] t= > Time Stepping Method: < SSP_Tools.Integrators.MSRK: MSRK 9s4k8p.mat priming=RK3 mini_dt_type=compatible, mini_dt_c=1.000000 > Spatial Discretization: < SSP_Tools.Discretizers.Spectral > Testing 10 Testing 14 Testing 20 Testing 24 Testing 30 Testing 34 Testing 40 Testing 44 Convergence Test Results Problem: Advection Equation u_t - -1*u_x = 0 u(x,0)=@(x)sin(4*pi*x) T=1.000000 Spatial Discretization: Spectral Fourier Collocation Method Time-Stepping Method: MSRK 9s4k8p.mat ---------------------------------------------------- N | dt | L1Error | L1Order | L2Error | L2Order | LinfError | LinfOrder | 10 | 0.0400 | 5.62e-07 | - | 6.09e-07 | - | 8.46e-07 | - | 14 | 0.0286 | 3.91e-08 | 7.92 | 4.28e-08 | 7.89 | 5.92e-08 | 7.90 | 20 | 0.0200 | 2.22e-09 | 8.04 | 2.52e-09 | 7.94 | 3.35e-09 | 8.05 | 24 | 0.0167 | 5.39e-10 | 7.77 | 5.90e-10 | 7.96 | 7.96e-10 | 7.88 | 30 | 0.0133 | 9.01e-11 | 8.02 | 9.97e-11 | 7.97 | 1.39e-10 | 7.83 | 34 | 0.0118 | 3.32e-11 | 7.98 | 3.67e-11 | 7.97 | 5.13e-11 | 7.96 | 40 | 0.0100 | 9.14e-12 | 7.94 | 1.01e-11 | 7.95 | 1.40e-11 | 8.00 | 44 | 0.0091 | 4.21e-12 | 8.14 | 4.69e-12 | 8.04 | 6.51e-12 | 8.01 | l2_errors = 1.0e-06 * 0.609203453000498 0.042821850973655 0.002521026421959 0.000590357275573 0.000099656432487 0.000036749084554 0.000010092480076 0.000004689437069 PDE Convergence Test Problem: < SSP_Tools.TestProblems.Advection: @(x)sin(4*pi*x) [0, 1] t= > Time Stepping Method: < SSP_Tools.Integrators.MSRK: MSRK 9s4k9p.mat priming=RK3 mini_dt_type=compatible, mini_dt_c=1.000000 > Spatial Discretization: < SSP_Tools.Discretizers.Spectral > Testing 10 Testing 14 Testing 20 Testing 24 Testing 30 Testing 34 Testing 40 Testing 44 Convergence Test Results Problem: Advection Equation u_t - -1*u_x = 0 u(x,0)=@(x)sin(4*pi*x) T=1.000000 Spatial Discretization: Spectral Fourier Collocation Method Time-Stepping Method: MSRK 9s4k9p.mat ---------------------------------------------------- N | dt | L1Error | L1Order | L2Error | L2Order | LinfError | LinfOrder | 10 | 0.0400 | 3.61e-08 | - | 4.04e-08 | - | 5.57e-08 | - | 14 | 0.0286 | 1.81e-09 | 8.89 | 2.03e-09 | 8.89 | 2.87e-09 | 8.82 | 20 | 0.0200 | 7.68e-11 | 8.86 | 8.43e-11 | 8.91 | 1.21e-10 | 8.87 | 24 | 0.0167 | 1.50e-11 | 8.96 | 1.66e-11 | 8.92 | 2.32e-11 | 9.08 | 30 | 0.0133 | 2.00e-12 | 9.03 | 2.24e-12 | 8.96 | 3.21e-12 | 8.86 | 34 | 0.0118 | 6.65e-13 | 8.80 | 7.43e-13 | 8.83 | 1.06e-12 | 8.86 | 40 | 0.0100 | 1.96e-13 | 7.52 | 2.16e-13 | 7.61 | 3.54e-13 | 6.74 | 44 | 0.0091 | 2.11e-13 | -0.78 | 2.37e-13 | -1.01 | 4.04e-13 | -1.38 | l2_errors = 1.0e-07 * 0.403860190779282 0.020251364906473 0.000843206957730 0.000165757338883 0.000022422497331 0.000007425555167 0.000002156407483 0.000002373710530