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In this paper, we apply second kind Chebyshev polynomials to solve variable-order linear cable equations. First, we convert second kind Chebyshev polynomials on the interval [−1, 1] into [0, R]. Then we reduce variable-order linear cable equation to a set of algebraic equations by using second kind shifted Chebyshev polynomials and collocation method. To obtain an approximate solution of the linear cable equation, we should solve this algebraic system. The results demonstrate that the proposed method has high accuracy and effectiveness for solving the variable-order linear cable equations. The validity and effectiveness of the method are demonstrated by solving several numerical examples.

NUMERICAL SOLUTION FOR VARIABLE-ORDER LINEAR CABLE EQUATIONS WITH SHIFTED SECOND KIND CHEBYSHEV POLYNOMIALS