Approximate Solutions to Three-Point Boundary Value Problems with Two-Space Integral Condition for Parabolic Equations

摘要

We construct a novel reproducing kernel space and give theexpression of reproducing kernel skillfully. Based on the orthogonal basis ofthe reproducing kernel space, an efficient algorithm is provided firstly to solvea three-point boundary value problem of parabolic equations with two-spaceintegral condition. The exact solution of this problem can be expressed bythe series form. The numerical method is supported by strong theories. Thenumerical experiment shows that the algorithm is simple and easy to implementby the common computer and software.