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a want to code implicite scheme for PDEs

u_t =a laplace u + L p_t

p_t = laplace p + u

pls help

I made a classical FEM discretization, but i dont know how to programe it.

(u^{(n+1)}_{ij}- u^{n})/t = a ((u^{(n+1)}_{(i-1j)}-2 u^{(n+1})_{(ij)}+u^{(n+1)}_{(i+1 j)})

/x^{2}+ (u^{(n+1})_{(i j-1)}-2u^{(n+1)}_{(ij)}+ u^{(n+1)}^{( i j+1 )}/y^{2}) +L (p^{(n+1)}

-p^{n})/t

(p^{(n+1)}_{ij}- p^{n})/t = ((p^{(n+1)}_{(i-1j)}-2 p^{(n+1)}_{(ij)}+p^{(n+1)}_{(i+1 j)})

/x^{2}+ p^{(n+1)}_{(i j-1)}-2p^{(n+1)}_{(ij)}+ p^{(n+1)}_{( i j+1 )}/y^{2}) + u^{n}

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