Abstract
A space W 2 1 [ a , b ] , which is proved to be a reproducing kernel space with simple reproducing kernel, is defined. The expression of its reproducing kernel function is given. Subsequently, a class of linear Volterra integral equation (VIE) with weakly singular kernel is discussed in the new reproducing kernel space. The reproducing kernel method of linear operator equation A u = f , which request the image space of operator A is W 2 1 [ a , b ] and operator A is bounded, is improved. Namely, the request for the image space is weakened to be L 2 [ a , b ] , and the boundedness of operator A is also not required. As a result, the exact solution of the equation is obtained. The numerical experiments show the efficiency of our method.
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