i used the "SparseDirect" option in Linearsolve

I had succeeded to solve this problem, the computation took 5 minutes, yet due to the fact that this computation is only one iteration in the loop, i am intrestrd in speeding up the computations

The matrix consist terms of different order-ill conditioned. the ill conditioning is result from the physical problem so avoiding it is a chalenge. to solve similar but smaller problems required about 128 digits or more