Estimated order of convergence in time (left) and space (right) for different values of |$\alpha $| (rows) and |$s$| (columns) based on solutions to (6.1) with |$D(x,t) = (1+x^{2}+t^{2})^{-1}$|. Here, the base values of grid parameters are |$\tau = 2^{-9}$| and |$h = 2^{-6}$|
|$\alpha \backslash s$| . | 0.1 . | 0.25 . | 0.5 . | 0.75 . | 0.9 . |
---|---|---|---|---|---|
0.1 | 1.73 | 1.75 | 1.79 | 1.82 | 1.83 |
0.25 | 1.22 | 1.25 | 1.31 | 1.40 | 1.44 |
0.5 | 0.74 | 0.75 | 0.77 | 0.81 | 0.84 |
0.6 | 0.64 | 0.65 | 0.66 | 0.68 | 0.70 |
0.7 | 0.70 | 0.69 | 0.70 | 0.68 | 0.66 |
0.8 | 0.80 | 0.80 | 0.80 | 0.80 | 0.79 |
0.9 | 0.94 | 0.93 | 0.92 | 0.91 | 0.90 |
|$\alpha \backslash s$| | 0.1 | 0.25 | 0.5 | 0.75 | 0.9 |
0.1 | 2.03 | 2.04 | 2.02 | 2.00 | 2.00 |
0.25 | 2.03 | 2.04 | 2.02 | 2.00 | 2.00 |
0.5 | 2.04 | 2.04 | 2.02 | 2.00 | 2.00 |
0.6 | 2.03 | 2.04 | 2.02 | 2.00 | 2.00 |
0.7 | 2.03 | 2.04 | 2.02 | 2.00 | 2.00 |
0.8 | 2.03 | 2.03 | 2.02 | 2.00 | 2.00 |
0.9 | 2.02 | 2.03 | 2.01 | 2.00 | 2.00 |
|$\alpha \backslash s$| . | 0.1 . | 0.25 . | 0.5 . | 0.75 . | 0.9 . |
---|---|---|---|---|---|
0.1 | 1.73 | 1.75 | 1.79 | 1.82 | 1.83 |
0.25 | 1.22 | 1.25 | 1.31 | 1.40 | 1.44 |
0.5 | 0.74 | 0.75 | 0.77 | 0.81 | 0.84 |
0.6 | 0.64 | 0.65 | 0.66 | 0.68 | 0.70 |
0.7 | 0.70 | 0.69 | 0.70 | 0.68 | 0.66 |
0.8 | 0.80 | 0.80 | 0.80 | 0.80 | 0.79 |
0.9 | 0.94 | 0.93 | 0.92 | 0.91 | 0.90 |
|$\alpha \backslash s$| | 0.1 | 0.25 | 0.5 | 0.75 | 0.9 |
0.1 | 2.03 | 2.04 | 2.02 | 2.00 | 2.00 |
0.25 | 2.03 | 2.04 | 2.02 | 2.00 | 2.00 |
0.5 | 2.04 | 2.04 | 2.02 | 2.00 | 2.00 |
0.6 | 2.03 | 2.04 | 2.02 | 2.00 | 2.00 |
0.7 | 2.03 | 2.04 | 2.02 | 2.00 | 2.00 |
0.8 | 2.03 | 2.03 | 2.02 | 2.00 | 2.00 |
0.9 | 2.02 | 2.03 | 2.01 | 2.00 | 2.00 |
Estimated order of convergence in time (left) and space (right) for different values of |$\alpha $| (rows) and |$s$| (columns) based on solutions to (6.1) with |$D(x,t) = (1+x^{2}+t^{2})^{-1}$|. Here, the base values of grid parameters are |$\tau = 2^{-9}$| and |$h = 2^{-6}$|
|$\alpha \backslash s$| . | 0.1 . | 0.25 . | 0.5 . | 0.75 . | 0.9 . |
---|---|---|---|---|---|
0.1 | 1.73 | 1.75 | 1.79 | 1.82 | 1.83 |
0.25 | 1.22 | 1.25 | 1.31 | 1.40 | 1.44 |
0.5 | 0.74 | 0.75 | 0.77 | 0.81 | 0.84 |
0.6 | 0.64 | 0.65 | 0.66 | 0.68 | 0.70 |
0.7 | 0.70 | 0.69 | 0.70 | 0.68 | 0.66 |
0.8 | 0.80 | 0.80 | 0.80 | 0.80 | 0.79 |
0.9 | 0.94 | 0.93 | 0.92 | 0.91 | 0.90 |
|$\alpha \backslash s$| | 0.1 | 0.25 | 0.5 | 0.75 | 0.9 |
0.1 | 2.03 | 2.04 | 2.02 | 2.00 | 2.00 |
0.25 | 2.03 | 2.04 | 2.02 | 2.00 | 2.00 |
0.5 | 2.04 | 2.04 | 2.02 | 2.00 | 2.00 |
0.6 | 2.03 | 2.04 | 2.02 | 2.00 | 2.00 |
0.7 | 2.03 | 2.04 | 2.02 | 2.00 | 2.00 |
0.8 | 2.03 | 2.03 | 2.02 | 2.00 | 2.00 |
0.9 | 2.02 | 2.03 | 2.01 | 2.00 | 2.00 |
|$\alpha \backslash s$| . | 0.1 . | 0.25 . | 0.5 . | 0.75 . | 0.9 . |
---|---|---|---|---|---|
0.1 | 1.73 | 1.75 | 1.79 | 1.82 | 1.83 |
0.25 | 1.22 | 1.25 | 1.31 | 1.40 | 1.44 |
0.5 | 0.74 | 0.75 | 0.77 | 0.81 | 0.84 |
0.6 | 0.64 | 0.65 | 0.66 | 0.68 | 0.70 |
0.7 | 0.70 | 0.69 | 0.70 | 0.68 | 0.66 |
0.8 | 0.80 | 0.80 | 0.80 | 0.80 | 0.79 |
0.9 | 0.94 | 0.93 | 0.92 | 0.91 | 0.90 |
|$\alpha \backslash s$| | 0.1 | 0.25 | 0.5 | 0.75 | 0.9 |
0.1 | 2.03 | 2.04 | 2.02 | 2.00 | 2.00 |
0.25 | 2.03 | 2.04 | 2.02 | 2.00 | 2.00 |
0.5 | 2.04 | 2.04 | 2.02 | 2.00 | 2.00 |
0.6 | 2.03 | 2.04 | 2.02 | 2.00 | 2.00 |
0.7 | 2.03 | 2.04 | 2.02 | 2.00 | 2.00 |
0.8 | 2.03 | 2.03 | 2.02 | 2.00 | 2.00 |
0.9 | 2.02 | 2.03 | 2.01 | 2.00 | 2.00 |
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