GATE CE 2019 Set 1 — Question 37

MCQ+2 / -0.67Easy1D Diffusion EquationPartial Differential EquationsEngineering MathematicsNumerical DifferentiationNumerical Integration & ODEs

Engineering Mathematics → Numerical Integration & ODEs → 1D Diffusion Equation

Last updated 5 September 2026

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\frac{v_i^{(n+1)} - v_i^{(n)}}{\Delta t} = \beta \left[ \frac{v_{i+1}^{(n)} - 2v_i^{(n)} + v_{i-1}^{(n)}}{(\Delta x)^2} \right]

\frac{v_i^{(n+1)} - v_i^{(n)}}{\Delta t} = \beta \left[ \frac{v_{i+1}^{(n)} - 2v_i^{(n)} + v_{i-1}^{(n)}}{2\Delta x} \right]

\frac{v_i^{(n)} - v_i^{(n-1)}}{\Delta t} = \beta \left[ \frac{v_{i+1}^{(n)} - 2v_i^{(n)} + v_{i-1}^{(n)}}{(\Delta x)^2} \right]

\frac{v_i^{(n)} - v_i^{(n-1)}}{2\Delta t} = \beta \left[ \frac{v_{i+1}^{(n)} - 2v_i^{(n)} + v_{i-1}^{(n)}}{2\Delta x} \right]

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\frac{\partial v}{\partial t}

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\frac{\partial v}{\partial t}

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