The article addresses the solution of systems of linear algebraic equations arising in static and steady-state vibration problems solved by the finite element method. A block-sparse matrix format based on the CSR (Compressed Sparse Row) format is presented, along with its GPU implementation using CUDA. A stabilized biconjugate gradient method is implemented and applied to model problems of varying dimensions; a comparison with a reference implementation in MATLAB is also conducted.

Keywords: sparse matrices, finite element method, block matrices, GPU, parallel computing, systems of linear algebraic equations, biconjugate gradient method

Brain neural networks models based on the model of Hodgkin-Huxley and the inhibitory and excitatory postsynaptic potentials EPSP and IPSP balance problem are investigated. The problem of the inhibitory and excitatory postsynaptic potential balance, affecting such person's ability as learning, memory, movement, ability to analyze and so on has great scientific and practical importance. Implementation of the model Hodgkin-Huxley in the Matlab environment is made. Model modification is considered given the occurrence of a synapse in neuron system.

Keywords: mathematical modeling, EPSP, IPSP, ionic channel, modified model parameter, neural network model, Hodgkin-Huxley