Of Bessel Transform Numerical Integration Research

Highly oscillatory integrals numerical method is a very important issue in science computing. Integrals involving Bessel-trigonometric transformation are difficult to calculate by the standard classic integration formulas in physics, chemistry, and engineering science. This paper studied the numerical methods in recent years and presented some new efficient methods to evaluate the quadratrue.Chapter one both the background and developments on the quadrature of highly oscillatory function have been presented.Chapter two Levin method for∫_a~bf(x)J_m(rx)dx has been discussedand the error analyze and some numerical examples have been showed.Chapter three two kinds of methods to solve problem like∫_a~bf(x)J_m(rq(x))dx has been discussed. One is Levin method, the other is generalized quadrature rules presented by Evans etc. This chapter shows the different from the two methods and analyzed which one is better.Chapter four the problem like∫_a~bf(x)cos(rx)J_m(rx)dx has been solved. The error estimations and some numerical examples have been presented. The new method has been proved the efficiency.