solving partial differential equations in the general case ( )-( )the coefficient matrix is an matrix with zero entriesexcept for ; ai; ai; ai; an; an; ( ( ( ( ( ( if we want to apply general methods for systems of odes on the form ut/we can assume linear utd ku the coefficient matrix is found from the right-hand side of ( )-( to be ; ki; ki; kn; kn; ki; ( ( ( ( ( ( we see that to implement the backward euler schemewe can either fill matrix and call linear solveror we can apply odespy we follow the latter strategy implicit methods in odespy need the matrix abovegiven as an argument jac (jacobian of in the call to odespy backwardeuler here is the python code for the right-hand side of the ode system (rhsand the matrix (kas well as statements for initializing and running the odespy solver backwardeuler (in the file rod_be py)def rhs(ut) len( rhs zeros( + rhs[ dsdt(tfor in range( )rhs[ (beta/dx** )*( [ + * [iu[ - ] ( [ ]trhs[ (beta/dx** )*( * [ - *dx*dudx( * [ ] ( [ ]treturn rhs