In this paper, we examined the two-point boundary value problems of the form L(y)=f(x,y) subject to the mixed boundary conditions y ' (a)-cy(a)=A,y ' (b)+dy(b)=B, where L is the differential operator (linear or nonlinear) involving partial derivatives of y, c≥0, d≥0, c+d>0, A and B are constants and x∈[a,b]. These equations are solved using weighted residual method. An approximating function with
... [Show full abstract] some constants is assumed to satisfy the boundary conditions. These constants are determined using various methods such as Galerkin method, collocation method, partition method, moment method and least-squares method. The results obtained from each method are compared with the analytical solutions.