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O Show the approximation of the second derivative in x and 8²4 2 2 h₁h3 P h3 (h1 +h3) (P3) - (nk) ~ əx² 2 P h₁ (h₁ + h3) (P₁) The approximation of second derivative en y-direction is: 2 2²6 h₂ h₁ 2 h₂ (h₂ + h₂) (P₂) following the stencil shown below, P₂ - (nk) ~ Əy² P3 h3 nk ha - -4(nk) + h₂ —Y(nk) + h₁ P₁ 2 ha (h₂ + H₂) (P₁) ha)

O Show the approximation of the second derivative in x and 8²4 2 2 h₁h3 P h3 (h1 +h3) (P3) - (nk) ~ əx² 2 P h₁ (h₁ + h3) (P₁) The approximation of second derivative en y-direction is: 2 2²6 h₂ h₁ 2 h₂ (h₂ + h₂) (P₂) following the stencil shown below, P₂ - (nk) ~ Əy² P3 h3 nk ha - -4(nk) + h₂ —Y(nk) + h₁ P₁ 2 ha (h₂ + H₂) (P₁) ha)

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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→ Show the approximation of the second derivative in x and 2²4 2 ax2 (nk) h₁h3 2 h₁ (h₁ + h3) Y (P₁) The approximation of second derivative en y-direction is: 2 2 dyž (nk) Oy2 (M) ~ m₂ (h₂²+ h₂) P (P₂) - 2 -p (nu) + hz -y(nk) h₂h4 ha (h2+ ha)P( following the stencil shown below, P₂0 = P₂ h₂ nk h₂ h₂ P₁ -4(nk) + h₁ 2 h3 (h₁ + h3) Y (P3) P₁ - (PA)
Transcribed Image Text:→ Show the approximation of the second derivative in x and 2²4 2 ax2 (nk) h₁h3 2 h₁ (h₁ + h3) Y (P₁) The approximation of second derivative en y-direction is: 2 2 dyž (nk) Oy2 (M) ~ m₂ (h₂²+ h₂) P (P₂) - 2 -p (nu) + hz -y(nk) h₂h4 ha (h2+ ha)P( following the stencil shown below, P₂0 = P₂ h₂ nk h₂ h₂ P₁ -4(nk) + h₁ 2 h3 (h₁ + h3) Y (P3) P₁ - (PA)
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