Interpolation Method for Solving Weakly Singular Integral Equations of the Second Kind
نویسندگان
چکیده
We establish a new straightforward interpolation method for solving linear Volterra integral equations with weakly singular kernels. The proposed is fundamentally different from all other published methods this type of equations. have modified some vector-matrix barycentric Lagrange formulas to be convenient interpolating the kernel twice concerning two variables and introducing ideas selecting nodes that ensure isolation singularity kernel. create rules distribution the do not allow denominator contain an imaginary value. interpolate unknown data functions into corresponding interpolant polynomial; each same degree via three matrices, one which monomial. By applying presented based on created rules, we transformed kernel into double interpolant polynomial equal function five which are monomials. substitute twice; left side right equation get algebraic system without collocation method. solution yields the coefficients matrix necessary find solution. solve different examples values upper integration variable. obtained results as shown in tables figures prove solutions extraordinarily faster to converge exact ones using interpolants lowest degrees give better results than those by other methods. This confirms originality potential method.
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ژورنال
عنوان ژورنال: Applied and computational mathematics
سال: 2021
ISSN: ['1683-3511', '1683-6154']
DOI: https://doi.org/10.11648/j.acm.20211003.14