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Novel functional matrix method using standard basis of polynomial linear space. (English) Zbl 1499.34154

Summary: This paper has developed a novel functional matrix using the standard basis of \((n+1)\) dimensional polynomial linear space to solve second-order singular initial and boundary problems. The linearly independent polynomials properties are used to convert the differential equations into algebraic equations with suitable solvers that can efficiently solve. Seven numerical examples are considered to demonstrate this technique’s applicability and efficiency. The obtained results are compared favorably with the exact solutions. Also, we proved some theorems on convergence, exact solutions, and uniform convergence.

MSC:

34B15 Nonlinear boundary value problems for ordinary differential equations
34A45 Theoretical approximation of solutions to ordinary differential equations
65L10 Numerical solution of boundary value problems involving ordinary differential equations
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