[\frac{{\partial w(x,t)}}{{\partial x}} | [W(i,k) = \frac{{W(i + 1,k) - W(i - 1,k)}}{{2h}} |
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[\frac{{\partial ^2 w(x,t)}}{{\partial x^2 }} | [W(i,k) = \frac{{W(i + 1,k) - 2W(i,k) + W(i - 1,k)}}{{h^2 }} |
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[\frac{{\partial ^3 w(x,t)}}{{\partial x^3 }} | [W(i,k) = \frac{{W(i + 2,k) - 2W(i + 1,k) + 2W(i - 1,k) - W(i - 2,k)}}{{2h^3 }} |
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[u(x,t)\frac{{\partial ^3 w(x,t)}}{{\partial x^3 }} | [W(i,k) = \sum\nolimits_{m = 0}^k W(i,k - m)\frac{{W(i + 2,k) - 2W(i + 1,k) + 2W(i - 1,k) - W(i - 2,k)}}{{2h^3 }} |
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[\frac{{\partial w(x,t)}}{{\partial x}}\frac{{\partial x^2 w(x,t)}}{{\partial x^2 }} | [W(i,k) = \sum\nolimits_{m = 0}^k \frac{{W(i + 1,k) - 2W(i,k) + W(i - 1,k)}}{{h^2 }}\frac{{W(i + 1,k - m) - W(i - 1,k - m)}}{{2h}} |
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[u(x,t)\frac{{\partial w(x,t)}}{{\partial x}} | [W(i,k) = \sum\nolimits_{m = 0}^k U(i,k - m)\frac{{W(i + 1,k) - W(i - 1,k)}}{{2h}} |
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w(x,t) = sinh(x) | W (x,t) = sinh(xi) |
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w(x,t) = cosh(x) | W (x,t) = cosh(xi) |