Aim: Deriving 4th order approximation of a 2nd order derivative using Taylor Table method Governing equations Central difference scheme(Symmetric scheme) Number of nodes in central schemes= p+q-1(p=order of derivative,q=order of approximation)                      …

Solution Equation of two-dimensional heat conduction equation is `frac{delT}{delt}=alpha**(frac{del^2T}{delx^2}+frac{del^2T}{delx^2})` where `alpha` is thermal diffusion coefficient. The equation is best described as a transient state two-dimensional heat conduction equation whereas if the time rate of change of temperature…

Aim: To compare the convergence rate (number of iterations) and transient (explicit and implicit) and justify the numerics involved. Abstract Equation of two-dimensional heat conduction equation is  `frac{delT}{delt}=alpha**(frac{del^2T}{delx^2}+frac{del^2T}{dely^2})` where `alpha`is the thermal diffusion coefficient.…

Aim: To understand the stability of the linear system using iterative techniques Abstract In the above case,  eigenvalues of [3 x 3] matrix are calculated by using iterative methods. The inbuilt command will not be used in this case. Governing equation: Let us consider a general [] 3 X 3 matrix which is of the form…