Boundary-value Problems in Mathcad

Boundary-value problems are different in Mathcad from Cauchy problem, as in a boundary-value problem the initial conditions are assigned at the ends of the interval of problem solving. To find a solution to such a problem false position method is in use in Mathcad system, when the initial condition in the right point of the interval is changed into the additional initial condition for the left point of the interval. After that a boundary-value problem is transformed into a Cauchy problem, methods of solving the latter discussed in the previous section. To realize the false position method in Mathcad function sbval is in use. This function determines the missing conditions in the initial point fortwo-point boundary problems. The function is characterized by the following syntax: sbval(z,a,b,D,load,score), where z is vector of approximations for the missing initial conditions at the left boundary; a,b –the left and the right boundaries of the interval of problem solving; D(x,y) is the vector-function, which contains the right segments of the first derivatives, written down in a character way; load(a,z) is the vector-function, which describes the initial conditions at the left boundary of the interval; score(b,y) is the vector-function used for assigning the right boundary conditions. The example of the boundary-value problem solution is shown in the programme listing. 

Boundary-value problems