The co-efficient matrix of linear second-order partial differential equations in the general form is partitioned with (n-1)x(n-1) submartices and is transformed into the block tridiagonal system. Then the cyclic odd-even reduction technique is applied to this system with the large-grain data granularity and the block cyclic reduction algorithm to solve unknown vectors of this system is created. But this block cyclic reduction technique is not suitable for the parallel processing system because of its parallelism chanigng at every computing stages. So a new algorithm for solving linear second-order partical differential equations is presentes by the block cyclic reduction technique which is modified in order to keep its parallelism constant, and to reduce gteatly its execution time. Both of these algoriths are compared and studied.