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3.4.E33

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Formula:1208
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MaRDI QIDQ1208

  • Label: 3.4.E33


Digital Library of Mathematical Functions ID 3.4.E33

∇ 4 ⁡ u 0 , 0 = 1 h 4 ⁢ ( 20 ⁢ u 0 , 0 - 8 ⁢ ( u 1 , 0 + u 0 , 1 + u - 1 , 0 + u 0 , - 1 ) + 2 ⁢ ( u 1 , 1 + u 1 , - 1 + u - 1 , 1 + u - 1 , - 1 ) + ( u 0 , 2 + u 2 , 0 + u - 2 , 0 + u 0 , - 2 ) ) + O ⁡ ( h 2 ) , superscript ∇ 4 subscript 𝑢 0 0 1 superscript ℎ 4 20 subscript 𝑢 0 0 8 subscript 𝑢 1 0 subscript 𝑢 0 1 subscript 𝑢 1 0 subscript 𝑢 0 1 2 subscript 𝑢 1 1 subscript 𝑢 1 1 subscript 𝑢 1 1 subscript 𝑢 1 1 subscript 𝑢 0 2 subscript 𝑢 2 0 subscript 𝑢 2 0 subscript 𝑢 0 2 Big-O superscript ℎ 2 {\displaystyle{\displaystyle\nabla^{4}u_{0,0}=\frac{1}{h^{4}}\,(20u_{0,0}-8(u_% {1,0}+u_{0,1}+u_{-1,0}+u_{0,-1})+2(u_{1,1}+u_{1,-1}+u_{-1,1}+u_{-1,-1})+(u_{0,% 2}+u_{2,0}+u_{-2,0}+u_{0,-2}))+O\left(h^{2}\right),}}


Constraint(s)

Symbols List

  • O ⁡ ( x ) Big-O 𝑥 {\displaystyle{\displaystyle O\left(\NVar{x}\right)}} : order not exceeding
  • u 𝑢 {\displaystyle{\displaystyle u}} : function
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