The block-by-block method,proposed by Linz for a kind of Volterra integral equations with nonsingular kernels,and extended by Kumar and Agrawal to a class of initial value problems of fractional differential equations...The block-by-block method,proposed by Linz for a kind of Volterra integral equations with nonsingular kernels,and extended by Kumar and Agrawal to a class of initial value problems of fractional differential equations(FDEs)with Caputo derivatives,is an efficient and stable scheme.We analytically prove and numerically verify that this method is convergent with order at least 3 for any fractional order indexα>0.展开更多
基金supported by the State Key Laboratory of Scientific and Engineering Computing,Chinese Academy of Sciences and by Hunan Key Laboratory for Computation and Simulation in Science and Engineering,by National Natural Science Foundation of China(Grant Nos.60931002,11001072 and 11026154)partially by the Spanish Ministry of Science and Innovation under Grant AYA2009-14212-C05-05.
文摘The block-by-block method,proposed by Linz for a kind of Volterra integral equations with nonsingular kernels,and extended by Kumar and Agrawal to a class of initial value problems of fractional differential equations(FDEs)with Caputo derivatives,is an efficient and stable scheme.We analytically prove and numerically verify that this method is convergent with order at least 3 for any fractional order indexα>0.
