please solve this problem manually

course :numerical mathods

Consider the following EDP distribution of heat in a body. x22T+y22T=0 a) Classify the type of this equation (Parabolic, elliptic, hyperbolic) b) Assuming x=y, use the finite difference approximation to write Laplacian difference Equation: Ti+1,j4Ti,j+Ti1,j+Ti,j+1+Ti,j1=0 c) Use Liebmann's method to solve the temperature distribution for heated plate (see below Fig.) subject to fixed boundary conditions. Employ over relaxation with a value of 1.5 for the weighting factor () and iterate to S=1%.5 grids, is divide the sheet. Liebmann's method: Ti,j=4Ti+1,j+Ti1,j+Ti,j+1+Ti,j1 For the first iteration Consider Ti, old=0 for unknown values Tijaw=Tijaw+(1)Ti,j1/ where Tij and Ti,jold are the values of Ti, from the present and the previous iteration, respectively, and is a weighting factor that is set between I and 2 . d) Compare your result with the solution provided in below figure Consider the following EDP distribution of heat in a body. x22T+y22T=0 a) Classify the type of this equation (Parabolic, elliptic, hyperbolic) b) Assuming x=y, use the finite difference approximation to write Laplacian difference Equation: Ti+1,j4Ti,j+Ti1,j+Ti,j+1+Ti,j1=0 c) Use Liebmann's method to solve the temperature distribution for heated plate (see below Fig.) subject to fixed boundary conditions. Employ over relaxation with a value of 1.5 for the weighting factor () and iterate to S=1%.5 grids, is divide the sheet. Liebmann's method: Ti,j=4Ti+1,j+Ti1,j+Ti,j+1+Ti,j1 For the first iteration Consider Ti, old=0 for unknown values Tijaw=Tijaw+(1)Ti,j1/ where Tij and Ti,jold are the values of Ti, from the present and the previous iteration, respectively, and is a weighting factor that is set between I and 2 . d) Compare your result with the solution provided in below figure