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Approximate Solution of Bratu Differential Equations Using Trigonometric Basic Functions

In this paper, I have proposed a method for ﬁnding an approximate function for Bratu diﬀerential equations (BDEs), in which trigonometric basic functions are used. First, by deﬁning trigonometric basic functions, I deﬁne the values of the transformation function in relation to trigonometric basis functions (TBFs). Following that, the approximate function is deﬁned as a linear combination of trigonometric base functions and values of transform function which is named trigonometric transform method (TTM), and the convergence of the method is also presented. To get an approximate solution function with discrete derivatives of the solution function, we have determined the approximate solution function which satisﬁes in the Bratu diﬀerential equations (BDEs). In the end, the algorithm of the method is elaborated with several examples. In one example, I have presented an absolute error comparison of some approximate methods.