Civil Engineering > GATE 2019 SET-1 > Numerical Analysis
A one-dimensional domain is discretized into N sub-domains of width Δx with node numbers i = 0, 1, 2, 3,..., N. If the time scale is discretized in steps of Δt, the forward-time and centered-space finite difference approximation at ith node and nth time step, for the partial differential equation ∂v/∂t = β(∂2v/∂x2) is
A
(vin+1 - vin) / Δt = β * (vi+1n - 2vin + vi-1n) / Δx2
B
(vin - vin-1) / Δt = β * (vi+1n - 2vin + vi-1n) / Δx2
C
(vin+1 - vin-1) / (2Δt) = β * (vi+1n - 2vin + vi-1n) / Δx2
D
(vin+1 - vin) / Δt = β * (vi+1n+1 - 2vin+1 + vi-1n+1) / Δx2

Correct : a

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