Crank Nicolson method convert parabolic pde into
Answers
Crank Nicolson method is a finite difference method used for solving heat equation and similar partial differential equations. This method is of order two in space, implicit in time, unconditionally stable and has higher order of accuracy.
Answer:
The parabolic partial differential equation (PDE) in one dimension is studied using an implicit Finite Difference technique. When compared to the Explicit Finite Difference approach, the Crank Nicolson scheme gives a superior truncation error for both temporal and spatial dimensions. Furthermore, the system is constant and always stable.
The relatively high computing cost of implicit techniques in the solution process is one disadvantage, however, this is offset by the high degree of accuracy of the approximate solution and the numerical scheme's efficiency. The Crank Nicolson strategy is used to solve a physical issue modelled by the heat equation with the Neumann boundary condition.
When we compare the numerical and analytical solutions, we see that the relative error grows dramatically near the right boundary, but then decreases as the spatial step size approaches zero.