Abstract
The shifted Jacobi polynomial functions approximation is extended to solving the linear ordinary differential equation of the two-point boundary value problem. The linear ordinary differential equation of boundary value problems is reduced to the linear functional differential equation of the initial value problem. A new time-domain approach to the derivation of a Jacobi transformation matrix together with the Jacobi integration matrix, the solution of the linear functional ordinary differential equation of the initial value problem can be obtained via shifted Jacobi series. Two examples are demonstrated and the satisfactory computational results are compared with those of the exact solution.
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