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Stochastic equation are one of the most important and applied topics in today, s world. It arises in modelling of different problems in science such as mathematics, finance, physics, mechanics, biology and so on. In many cases they have no explicit form of the solution, so numerical methods come to solve the problem and find an appropriate approximation. Different basis functions have been used to find an approximation such as block pulse functions, hat functions, hybrid functions, wavelet methods and so on. We use both modified hat functions (MHFs) and improved hat functions (IHFS) and their operational matrices to find approximations for the original equation: X(t) =f(t)+∫<subscript>0</subscript>^tμ(s, t)X(s)ds +∑<subscript>j=1</subscript>ⁿ∫<subscript>0</subscript>^tσ<subscript>j</subscript>(s, t)X(s)dB<subscript>j</subscript>(s), where s, t ∈ D =[0,1), X, f, μ,σ j, j=1, ..., n are the processes defined on the same probability space (Ω, F, P) and X is unknown. Also ∫<subscript>0</subscript>^t μ (s,t)X(s)ds, ∫<subscript>0</subscript>^tσj(s,t)X(s)dBj(s), j=1, ..., n are Ito integrals and B(t) is a Brownian motion. stochastic Material and methods In this scheme, we expand all known and unknown functions in terms of basis functions and replace in the original equation. The operational matrices of both bases are calculated and embedded in the equation to achieve a linear system of equations which give the expansion coefficients of the solution. Results and discussion We consider some examples to show the accuracy and simplicity of these two methods, then compare the proposed method with other methods. Moreover, according to error analysis and reported results, we conclude that the proposed method were in a good agreement with the exact solution. Conclusion The following conclusions were drawn from this research. The approximate solution can be easily calculated by solving a linear system of equations and using Matlab ۷. Convergence and error analysis show the reliability and accuracy of these methods. [ABSTRACT FROM AUTHOR]

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