Symbolic Computation Group

Solving initial value problems and boundary value problems of linear ODEs plays an important role in many applications. There are various numerical methods and solvers to obtain approximate solutions typically represented by points. However, few works about global error estimation and optimal solution to minimize the residual can be found in the literature.

In this talk, we first use cubic Hermite spline interpolation at mesh points to represent solutions, then we define the residual and related errors. An error estimation is given to control the global error by residual in this talk. Thus, solving linear ODEs is reduced to an optimization problem for minimal residual in curtain solution space which can be solved by conjugate gradient method with taking advantages of the corresponding highly structured matrix.