To avoid computation of multi-frequencies pressure in solution of frequency method, a dual reciprocity method (DRM) is applied to convert domain integral, which is related to derivatives of pressure over time, in boundary integral equation into boundary integral. Firstly, field points are collocated at all boundary nodes. With boundary condition, boundary quantities at boundary nodes can be represented linearly by quantities at domain nodes, which are applied for radial basis function interpolation and are arbitrarily distributed in DRM. Secondly, field points are further collocated at domain nodes. A system of ordinary differential equations (ODEs) of the second order is obtained. Thirdly, variation rate of pressure was introduced as an unknown quantity to reduce order of resulted ODEs. Finally, a precise integration method is adopted to solved the first ordered ODEs. Numerical examples demonstrated validity and stability of the method.

Since refractory states of an excitable medium can be excited,depolarization is introduced into the Bar model.Depolarization effects on spiral waves are investigated.It shows that as threshold of depolarization and depolarization duration are chosen suitably,depolarization can induce drifting and meandering of spiral wave and even cause spiral wave moving out of boundary of the system.The dense spiral wave,two-arm spiral wave,twin speaks wave,multiple spiral wave and spatiotemporal chaos can also be generated with depolarization.Physical mechanism underlying these phenomena is discussed.

Laminar free convection heat transfer of non-Newtonian power law fluids over a vertical flat plate has been studied.It is a problem of nonlinear two point boundary values.The two-system of partial differential equations for velocity and temperature are coupled and nonlinear. Three numerical methods are also used to calculate the problem.The effects of Prandtl numbers(Pr) and various flow indexes on convection heat transfer(Nu) have been discussed and the calculations are compared with each other and with the results of other papers.