Application of the Method of Straight Lines for Solving Parabolic Equations with Arbitrary Linear Boundary Conditions

A method for applying the straight-line technique by transforming a problem with arbitrary linear boundary conditions into a Dirichlet problem is developed. Assuming the boundary values of the desired function are given, the Dirichlet problem is solved. The actual boundary values of the desired functions are found by aligning the assumed boundary values with the newly obtained values according to boundary condition approximations. These values are then used to implement the straight-line method, ensuring second-order accuracy for equation and boundary condition approximations.