In this work, we present a fourth-order scheme based on hyperbolic approximated fuzzy components and compact discretization to solve two-point boundary value problems. The combination of compact discretization and fuzzy transform yields a more efficient approach with sixth-order local truncation error having fourth-order solution accuracies. Fuzzy components are approximated with a three-point algebraic combination of solution values. The proposed configuration generates a tridiagonal Jacobian matrix, reducing computing time and memory space. The scheme is evaluated for error bounds such as root-mean-square and maximum absolute errors. To assess the utility and efficiency of the proposed scheme, we present numerical simulations of linear and nonlinear second-order boundary value problems.

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A Hyperbolic Basis Fuzzy Component Scheme for Two-Point BVPs

  • Kritika,
  • Navnit Jha

摘要

In this work, we present a fourth-order scheme based on hyperbolic approximated fuzzy components and compact discretization to solve two-point boundary value problems. The combination of compact discretization and fuzzy transform yields a more efficient approach with sixth-order local truncation error having fourth-order solution accuracies. Fuzzy components are approximated with a three-point algebraic combination of solution values. The proposed configuration generates a tridiagonal Jacobian matrix, reducing computing time and memory space. The scheme is evaluated for error bounds such as root-mean-square and maximum absolute errors. To assess the utility and efficiency of the proposed scheme, we present numerical simulations of linear and nonlinear second-order boundary value problems.