The utilization of a parallel processor such as the graph-ics processing unit (GPU) is only natural for the simulation of spikingneural p systems (SN P Systems) because of their inherent parallel na-ture. A recent work, created an SN P system simulator, GPUSnapse,that both utilizes GPU and runs on modern web browsers by exploitingthe Web Graphics Library (WebGL) which creates shaders to generatetextures that corresponds to SN P system simulation algorithms. Ma-trix representation operations were used in GPUSnapse. In GPUSnapse,when working with large matrices a common concern are sparse matri-ces. Sparse matrices are known to downgrade the performance of thesimulation because of wasting memory and time due to performing re-dundant operations. In this work we extend GPUSnapse by: (a) usingoptimized sparse matrix operations to improve the performance of oursimulator and; (b) increase the number of neurons that can be handledby the simulator due to better memory usage. We also identify the lim-itations of GPUSnapse in terms of the sizes of each benchmark systemthat it can handle. We present two algorithms: deterministic and non-deterministic algorithms, which we use to compare the performance andmemory requirements of the previous GPUSnapse and our present work.We also analyzed the performance between GPU and CPU implementa-tions of all algorithms involved. Results from our work show promisingimprovements such as up to a 1.97x speedup of GPU runtime and up to 30% reduction of memory usage. We also identify some bottlenecks inour work and recommendations for improvements.