Solution of a barrier option Black-Scholes model based on projected differential transformation method

In this article, the solution of the linear variant of a Barrier Option Black-Scholes Model (BOBSM) is considered via a semi-analytical approach referred to as the Projected Differential Transformation Method (PDTM). Similar to the traditional Differential Transformation Method, this new approach demonstrates feasible progress and efficiency of operation. For simplicity of illustrative, the BOBSM is converted to an equivalent heat-like form, and a series-form of the solution (root) is successfully obtained. Hence the PDTM is suggested for both pure and functional sciences for strongly nonlinear differential models with financial applications.