Due to its capacity to offer high-performance computing solutions for a variety of applications, hybrid multicore algorithms (HMAs) have grown in popularity in recent years. In this article, we offer a study on the use of HMAs to graphs and certain semi-numerical applications. We specifically look at how well HMAs perform in two different kinds of applications: graph algorithms and semi-numerical simulations. In terms of graph algorithms, we take into account a number of well-known issues, such as shortest path, minimal spanning tree, and graph clustering techniques. We put these algorithms into practise utilising both conventional CPU-based parallelization approaches and HMAs, and we evaluate how well they work with various graph sizes. We explore the challenge of employing partial differential equations to simulate the behaviour of complicated systems, such as fluid flow, for semi-numerical simulations (PDEs). We put into practise a hybrid strategy that combines GPU acceleration with CPU-based parallelization approaches, and we evaluate its performance against more conventional CPU-based parallelization strategies. showed both graph algorithms and semi-numerical simulations may significantly outperform conventional CPU-based parallelization strategies when using HMAs. In particular, HMAs can boost performance for graph algorithms up to a factor of two and for semi-numerical simulations up to a factor of five. Our findings show the potential of HMAs as a formidable tool for high-performance computing in graph algorithms and semi-numerical applications.